I'll be straight up with my opinion here: Yes, it is.
Now, you can disagree with me, but before you shake your head and say, "No, Kristan, there's no way the two are related. Come on..." let me argue my point for a minute, but before we get to that, let's define what each genre is.
What is a Western?
A Western is a film, television drama, or novel about cowboys in western North America, set especially in the late 19th and early 20th centuries. - The Oxford Dictionary
This can make it pretty easy to spot. It's the "Old West". Cowboys. Ranches. The OK Corrall and John Wayne in chaps and the complex saddles and bridles on numerous horses. Even the fabled Zorro could be argued as being at least semi-Western, if with very heavy Spanish influences.
The premise of a western is simple and easy to follow. But is that all there is to it?
In detail, though, the full definition of how to define the genre itself has the following elements:
Self-reliances, usually by the hero (or even anti-hero)
"Justice", either in the form of gathering a posse to hunt down an outlaw or a representative of the law doing it - or even anti-hero "outlaws" doing the right thing for the right reason but bending the rules at the same time.
There is usually a "us vs. them" story. Law vs. Outlaw, etc.
It's a rough country and "civilization" is somewhere not quite where the action takes place. Westerns are famous for taking place in what is considered a new frontier.
Horses and cowboys, and technology as we know it is barely present. There could be a telegraph, but no phones or rapid method of communication.
Whatever the society is in the story, it needs the help of an independent outsider (think Clint Eastwood's character in The Good, The Bad, and the Ugly) or even a "lawman" to fight for and/or lead them vs whoever their foe is (usually a large gang of robbers or other harmful outlaws).
Decreasing government presence, which goes with "civilization being over there".
A harsh, wild, and wide-open landscape. The roles of hero, victim, and villain are clearly defined with no room for ambiguity.
There is always a "clock" which is the time limit the hero of the story has to complete their mission of saving the victim or fighting off the villain.
The conflict is close and personal to the protagonist.
Now that we've listed the elements of the western, you can probably think of a few more examples that fit the bill.
But how does the Western compare to Post-Apocalyptic?
How do you define Post-Apocalyptic?
Apocalyptic and post-apocalyptic fiction is a subgenre of science fiction, science fantasy, dystopia, or horror in which the Earth's technological civilization is collapsing or has collapsed.
- The Oxford Dictionary
On the surface, they look very different. After all, the video game series Fallout, as well as Stephen King's The Stand, has to be different, right?
Let's take a look:
The setting is fantastical (nuclear apocalypse, pandemic, meteor strike, economic collapse, etc) but rooted in "what could happen".
Based after a fictional fall of civilization.
If there is a government, it's "over there" (wait a minute, where have we seen this before?).
Usually requires horses or another primitive way of getting around as whatever the modern way of doing so is no longer readily available (huh...)
Survivors need the help of an independent "outsider" (getting more familiar by the second...) , or help comes from within from a strong, independent type, to fight for and/or lead them.
Harsh, wild, possibly wide-open landscape depending on why civilization ended.
Hero, victim, and villain not always clearly defined.
Usually a "clock", or definite time limit for the protagonist to take action.
The Similarities Between the Two
In the two lists, the similarities should have jumped out at you.
While the background of why the settings are the way they are are vastly and radically different, the outcome is startlingly similar.
Civilization is "Over There", Presuming It's There At All
In both cases, civilization is "over there". It's not close, and this is presuming there is something of civilization in the case of post-apocalyptic. Even in the case of the Western, civilization itself is far enough away that it may as well not exist.
The towns are spread far apart and are generally independent of each other, or outright competing with each other, with only tenuous contact between them. This is similar to how towns and settlements in post-apocalyptic act to each other only, unlike in a Western where a "lawman" can show up and does have authority, the only law in a post-apocalyptic story is what that town decides to acknowledge or is forced on them by someone stronger.
By Foot or By Horse - But Not By Car
In both cases, unless there is a glimmer of advancement kept in the case of the post-apocalyptic story (think The Hunger Games here, there is a central city with all of the technology and then the outlying areas get the cast-offs if anything at all), transportation and the ability to communicate between towns and settlements is very limited.
The most common way of getting around is on foot (which seems to be a common theme in post-apocalyptic, especially if zombies enter the picture) or on a horse (which happens more often in Westerns), however, in both genres, it can go either way.
You can have the protagonists riding on horses in a post-apocalyptic story and a gunfighter on foot in a Western... but don't expect widespread use of cars or other conveyances. Even trains are somewhat rare in both genres.
The Independent Protagonist
Another common theme is the plucky, and independent, protagonist.
In a Western, the protagonist is usually the hero and he (or she) isn't from the town. If they are, they are the prodigal and returning child after maybe completing the Hero's Journey. Or not. Who knows? They just weren't in the town when the proverbial kaka hit the fan but have conveniently enough shown up right in the nick of time to solve it all... or die trying.
In a Post-Apocalyptic story, it could go either way. It could be just like in a Western where the protagonist wandered into the area (like in Fallout 3 or Fallout 4) somehow, or they were there the whole time and needed a push to start (like in the Hunger Games). Either way, there is something about them that makes them independent and they probably would have left on their own eventually anyway to discover what is out there.
The only exception here is Zorro, but Zorro is a special case. He is from the town, but no one knows who is under the mask - and if they did, they probably wouldn't believe it. However, this still makes him an independent outsider as it's the mask, outfit, and the horse that takes him outside of his normal life as Diego de la Vega and into the outsider role of Zorro.
The Time Limit
In almost every story, whether Western or Post-Apocalyptic, there is a time limit to complete whatever the "mission" is that the protagonist needs to do before this time limit expires.
In a Western, it could be, as in The 3:10 to Yuma, only having so much time to get an outlaw from a town where he's been tried to the train taking him to jail while his outlaw gang tries to free him. It could be a matter of finding a water source before the town dies out due to drought or any number of things.
Similarly, in a Post-Apocalyptic story, there is the time limit. In the Walking Dead, it's usually finding shelter or food, or something, before the zombies get the survivors. In Good Omens, the angel and the demon team up to raise the Anti-Christ in a balanced way to prevent the apocalypse, but when they lose him they have to find him again before the Four Horseman causes it. There could also be the issue of survival as food shortages and solving that before people starve is also a common theme.
Where they split off and become two different genres
Beyond the obvious of one being set in a real-time period that actually happened (The Western) and the other on a fictional collapse of society somewhere in the near, not so near, or even distant future (Post-Apocalyptic), there are some other differences that separate them.
The Root Cause
A Western is a romanticized, and sometimes not very politically correct, take on a very real-time period that actually happened... and in a specific area of the world. It heavily favours and glorifies the US-based West and South-West and rarely strays from this. It's not so much a cause... unless you count the passage of time and advancement of technology.
The root cause of how people got there is also different. Civilization, as they knew it, ended and left them needing to survive in a decaying world. It's entirely fictional and hasn't happened, and the causes are usually fictional as well even if based entirely on something that could happen.
In short, a Western is based on something that did happen and Post-Apocalyptic on something that could happen but hasn't, even if the end result is the same.
Hero, Victim, Villain... Or All Three At Once?
In a Western, you know immediately on the opening of the movie who the bad guy is, who the good guy is, and who (or what) the good guy needs to save or protect. Even when the hero is reluctant, or even not exactly law-abiding... they're going to do the right thing. The villain will be out to stop them.
Clear and simple.
In Post-Apocalyptic stories, this isn't usually that clear cut. It can be but typically is more complex.
Sometimes the town or the person who is the "victim" isn't an innocent player deserving of being saved. The villain, if the story was from their perspective, could just as easily be the hero, and vice versa with the hero possibly being downright evil.
The video game The Last of Us is a great example of this. I won't spoil why, but if you've played the game you know exactly what I mean.
However, their motivations are clear - and understandable.
It's usually to just survive.
Why Does It Matter?
The Western started going out of vogue in the 70s and 80s, and Post-Apocalyptic started to take its place.
In my opinion, the Western genre has a problematic, and racist, history as some of the old Westerns were heavily based on the killing of Native Americans as barbarians out to kill the white pioneers, hence "Cowboys and Indians" being the cringe-worthy game children played when the Western genre was at its height of popularity in the 50s and 60s.
Later Westerns were more about the independent cowboy or gunfighter protecting the town against criminals, or just "human vs. environment" but, in my opinion, the damage was done.
By comparison, while Post-Apocalyptic fiction draws much from the same themes (and is perhaps the direct successor of the Western), it doesn't have the same problematic beginning. The protagonist can be anyone, from anywhere. The settlement needing protection can be any settlement, or none at all. The "vs. Them" element is more about disenfranchised criminals, bullies, and other less savoury characters deciding that working together in harmony wasn't their cup of tea rather than a racialized "vs. Them".
What also began to rise in popularity in the 70s and 80s were science fiction and fantasy. Star Wars played a huge role in blurring the lines with Han Solo, the penultimate scoundrel/gunfighter in space which, like Star Trek before it, kicked off a love affair in looking forward.
But people still love the Western-style feel of survival, independent heroes, and wide-open spaces. Given the comparison, it's my personal belief that the Post-Apocalyptic genre stepped in to fill the void left by the Western genres fade from glory.
Could The Western Come Back?
I think it already is back. We're seeing more and more "frontier" space stories (the prime example of this being the Borderlands series) and the blurring of lines between Post-Apocalyptic and Western.
And I really don't mind that at all.