First of all, please reread the title of this piece, because the phrasing is important. I'm saying Fight Club and Office Space are the same movie, not similar movies. The reason for this distinction is derived from the fact that, if I was only addressing the idea of these movies being similar, I would be approximately the 394,876th person to point this out on the internet. (You can read examples here, here, and here, just for starters.) Most of these pieces, however, also see The Matrix and/or American Beauty as being parallel with the first two as well, in that all four were released in 1999, and all four showcase a socially-stifled heterosexual white male stuck in a soul-crushing office job that's irreconcilable with the lofty life expectations he holds, before each has a profound realization that frees his consciousness from those old confines, and subsequently sets him on his journey to a new, more worthwhile reality.
This is why I'm only focusing on the first two films: while all four are indeed quite comparable, only Fight Club and Office Space are practically mirrors of each other, because they feature an identical thematic arc that both of their analogously-afflicted protagonists follow, from start to finish, which neither The Matrix nor American Beauty do.
The Suffocating Situations
This is the most obvious, repeatedly covered strand of their similarities. Both Office Space's Peter Gibbons and Fight Club's "Narrator" — who I will refer to as "Jack" for the rest of this piece — work mind-numbing jobs that pretty much have destroyed their will to live. Both also reside in cookie-cutter apartments, have unfulfilling social lives, and feel completely isolated from those they spend time with.
Most importantly, both seem to have totally accepted this reality for themselves at the outset, making no strides to change anything, no matter how miserable it makes them. Instead, Peter anesthetizes himself with a fantasy about doing nothing, while Jack spends his evenings pretending to have every terminal disease known to man, so that he can actually feel something and get people to listen to him.
So this is who they both are at the beginning: lonely men with a vague — yet acute — wish for things they don't know how and do nothing to get for themselves, who then placate themselves with dysfunctional routines just to get by. That's the starting point for both and, as such, they both desperately require an external jolt of some kind.
But please note how neither engages the respective women they're each clearly attracted to, which could easily serve as this motivating jolt. Peter refuses to ask out Joanna, the waitress he admits to having a major crush on, while Jack treats Marla, the one person he genuinely has something in common with (because she sincerely understands what he's seeking by attending those support groups), like some kind of leper, instead of just going with this obvious opportunity to connect.
Since neither is willing to do anything about their situation, or is able to recognize the people in their lives who might help, an intervention then becomes necessary. For Peter, this arrives through a kind of fate when a hypnosis exercise goes awry, leaving him totally relaxed and indifferent to the mundane hassles of his job/life. On the other hand, Jack's own brain unconsciously does the heavy lifting for him by creating a completely new personality to handle all this: one Tyler Durden.
But again, please notice how, no matter the specifics of their respective change, the end result for each is functionally equivalent. In Tyler, Jack unintentionally creates both a friend for himself as well as the ideal avatar of himself, a guy who is both knowledgeable and motivated enough to make these vague, distant desires Jack has a reality (including hooking up with Marla). As Tyler even so famously tells him:
"You were looking for a way to change your life; you could not do this on your own. All the ways you wish you could be, that's me. I look like you wanna look; I f--k like you wanna f--k; I am smart, capable, and most importantly, I am free in all the ways that you are not."
Peter's imprinted devil-may-care attitude achieves this same end for its own previously impotent host. It allows him to finally speak from an authentic place to Joanna, behave at work like he's always wanted to, and just spend his limited time on the planet in a way he can finally enjoy.
Indeed, each protagonist's life is initially enriched by the incorporation of these new, drastically different personalities, in ways the two never thought possible. They're finally where they want to be in life. All seems well.
The Creations Get Out Of Hand
Here again, this idea gets played out differently between the two, while the idea itself is exactly the same. For Peter, his contempt for what his job both represents and made him feel fully merges with that previously beneficial nonchalance he received earlier, instilling in him a desire to steal back from the company he works for that which he feels owed, but now with no counterbalance of fear to keep this desire in check. Worse yet, he recruits his only two friends to join him in this crime, doing so while they're at their most vulnerable (i.e. after having just lost their jobs).
Likewise, Jack comes to realize Tyler is, in fact, him and, moreover, has been planning a coordinated act of financial terrorism against the creditors he believes keep so many as slaves to the system, especially Jack. Needless to say, this attack substantially crosses Jack's threshold of acceptability, forcing him to find any way he can of stopping it, and Tyler by extension. Through tremendous difficulty (and profound existential bewilderment), Jack pushes forward until he finally reaches his moment of truth: a showdown with Tyler, which is really his showdown with himself.
Going back to Peter, his moment of truth arrives after the criminal plan he hatched goes completely off the rails, leading to a situation where he and the two friends he brought into this are assuredly going to prison for what they've done. Just like Jack, Peter must finally face what has been done and was allowed to occur, and then deal with the person who set it all in motion. In other words, Peter also arrives at a showdown with himself.
Their Final Decisions
And one final time: Both characters make the exact same decision within their own distinct situation. Peter realizes he must take responsibility for all this; he can't hide from it behind his old unconcerned mental state, or allow the friends he involved in it to go down for his choices. So he withdraws the money he stole and gives it back, directly to the boss he can't stand, along with a letter fessing up to the whole thing. With no laid back hypnosis to now plow the road for him, Peter confronts his fears on his own and refuses to buckle underneath the weight. He stands on his own two feet, faces the music, and is willing to take what comes next on the chin.
Jack essentially does the same thing. By finally accepting Tyler is him and he is Tyler (i.e. that both Tyler and Tyler's actions are ultimately his responsibility), Jack also realizes he can't stop his alter ego without sacrificing himself; once he understands "the gun is in my hand," he's able to put it where it needs to go: his own mouth. By then pulling the trigger, Jack demonstrates he no longer needs Tyler to do what he can't; he too has finally fully confronted his fears, and refused to buckle. He also stands up, faces the music, and willingly absorbs what comes next without cushion.
And what happens to both, after these life-as-you-know-it-ending decisions? They're both okay — better than okay, actually. Peter gets bailed out by another act-of-god type development, which comes through chance like the hypnosis mishap that started him on his journey.
He ends up, not only still with Joanna (in a now much more honest and healthy relationship), but also doing what he felt was impossible at the start of the film: being happy — or at least content — with his job, simply by taking one that suits his interests and avoids everything he understandably despised about his old one. No earth-shattering breakthrough is (or ever was) required.
And his counterpart? He survives his monumental decision as well, since his willingness to shoot himself in the head didn't so much translate to any kind of proficiency in actually doing so (i.e. he managed to only catch himself in the cheek). But Tyler does die, because it was Jack's decision to (ostensibly) end himself that ended his initial, unconscious need for Tyler. And so Jack closes the film finally reaching out to the person he should've been reaching out to from the start.
The Shared Lesson
At the beginning of this post, I made the claim that Fight Club and Office Space were the same story, in that the arc of both main characters is identical. So what is this arc then? Simple: Stop being a baby; take responsibility for yourself; get over your silly disappointment with the realization that the mythologized life you were taught to expect was never real; adjust to the needs of your actual life like an adult; make the most of what you have in front of you; stop waiting on extreme situations, acts of god, or personal saviors to deliver you from your BS.
In two words: Grow up.