What is "Old School?" Well, I will start by quoting myself-
There was a specific movement in the very early early 2000s to clone rule-sets to enable people to play older versions of D&D. This was a specific response to the time that I think some people have forgotten (or newer players aren't aware of). In general, this first movement was a reaction against WoTC and 3e. In other words, because the older rulesets were not available (and WoTC would not make them available), people craving the "TSR" experience instead of 3e looked to make their own, compatible rulesets (whether for OD&D, B/X BECMI RC, 1e, or 2e). Moreover, we see the explicit use of the name "old school" in two of the most prominent of these rulesets- OSRIC is Old School Reference and Index Compilation. OSE is Old School Essentials. For that reason, initially Old School meant "TSR" era D&D. That said, I wouldn't say that the desire to clone (or clean up a little) the older rulesets necessarily carried a philosophical component. It was just people that were worried because their favorite games had disappeared, and they would rather play the older rules than the new-fangled 3e (at that time). Notably, this was specific to D&D, simply because it arose in a very narrow context of a new edition being released and older editions of D&D were not available (and would not be officially until 2012/13).
However, there is a separate component to this, which both involves the older rules (and retroclones) and stands independent from them. I haven't done a really deep dive on this, but I would say that, arguably, it rose to prominence as a reaction to 4e. I could be wrong, but the earliest documents related to Old School as a philosophical movement (such as Matt Finch's primer) date to 2008. Arguably, "old school" or "OSR" is best conceived when thinking of a specific set of ideas regarding "how to play" as a reaction against the direction of D&D- both 3e and 4e. Again, this is particular to D&D because it arose both as a reaction to the current "direction" of the game, and because it presented a "historical" version of the game as the way to play. This included ideas like- resource management, regular characters (not superheroes), unbalanced scenarios that the players would have to chose how to solve, a reliance on rulings by the DM as opposed to rules, and the idea of "player skill" not "character skill" (aka, "Skilled Play"). Usually, there would be additional bits added in (mapping, hirelings, etc.).
Notably, like all movements that call for a return to the past, it presents a unified, but false vision of what the past was. Obviously, and this should go without saying, the past is not a monolith. Anyone who lived through the time or has read histories (such as The Elusive Shift) knows that there was a vast variety of playing styles and approaches to OD&D in the 70s. While I think that OSR captures some concepts from then that have fallen out of favor in more modern games, it is also necessary to point out that it is certainly not true that every game back then was an attrition-based megadungeon crawl with 10' poles and disposable waves of hirelings. The sheer weirdness of the games is captured by the fact that so many early RPGs were, in fact, simply spinoffs of D&D (one of my favorite anecdotes is that Superhero 2044, the first superhero RPG published in 1977, was actually the campaign notes from an OD&D game where the characters went through a portal and met up with comic book heroes).
Unfortunately, when you have a style that is explicitly rooted in the the rejection of modern gaming, it will often attract people that are along for the ride not because they are rejecting the rules of modern games, but because they are rejecting the sensibility of the people that are playing. In other words, the nostalgic attraction isn't rooted in the simplicity of the rules or the belief that these rules better allow for a better game for their table, but instead a nostalgic attraction for a time when (in their opinion) they didn't have to worry about appropriation, or risque art, or inclusive play. The adoption of these rules, for some people, is a rejection of the modern and a political statement.
...which is unfortunate. I think that the vast majority of people attracted to OSR or "old school" games, specifically to the various retroclones and versions of D&D that seem to comprise the majority of the current "old school" market, just love aspects of the play or the rules. Others have stripped away the rulesets even more (this is FKR, which is just the latest iteration of "rules lite, DM adjudicates" that has been part of the hobby since the 70s as well).
So when people say "Old School," they are often referring to a number of different things. Usually, but not always, it is referring to D&D since the term originated there; but there are those who use it to refer to some early games like Traveller as well. Some people use it to refer to a philosophy of play, and others to rulesets only. Some people use it to refer to the entirety of TSR-era D&D, and other explicitly exclude some TSR output (usually 2e, sometimes post-Gygax 1e, sometimes everything that isn't OD&D).
For me, "Old School" (as opposed to OSR or FRK or other terms) is D&D, and D&D-compatible products, from 1974-1984. I would put the end of it in 1e with the publication of I6/DL1 and UA. I would say that while it isn't very different, B/X is old school, Metzer BECMI isn't, and the Rule Cyclopedia is certainly not. But that's me- and as time goes on, those distinctions will further collapse into meaninglessness as fewer people even understand those distinctions. Within the next five years, how many 5e players will know much about ... 3e? Let alone TSR-era D&D?