It does not matter what way it (breaking the game) is done. Glitched is a run that breaks something in the game and forces it to admit it was completed while it wasn't.
Glitched SMW does exactly that - makes the game admit it was completed and run its usual ending. Same with Contra 3, Battletoads, Kirby.
Crash Bandicoot breaks it in the middle, it makes it think all gems were collected (the only way to access the final boss) while none of them was. You don't complete the game without gems, but you cam make it think all gems are there. So its completion state is false gameplay-wise. But it's technically legit since it's the same as usual.
Super Metroid breaks the game to think all bosses were defeated while none of them was, and you don't beat the game without beating Mother Brain at least. The glitched run just sets some triggers somewhere and that's all.
In Megaman, the game completion state is gameplay-wise valid since you only skip some levels to their ends by manipulating lag, and play the very game level by level, beating bosses. But I'd call that a borderline case, which is not yet "glitch to game end". It's similar to "2P Warps" Battletoads, where you skip to level end by TASing the luck (this level skips to its end in real time consistently). SM64 abuses game physics to pass a checkpoint/whatever, the very game is untouched.
So the definition is pretty easy:
Is the game actually being completed, or soft-hacked into completion state? It's like, "I'm tired of playing it, let me just set certain bytes and drop it". Normally it can be done by hacking, but TASing allows to hack it in the legit way - input only.
Another difference: TAS as a
superplay is to complete the game with superhuman precision, what makes it interesting to follow. TAS as a
speedrun is to reach the end as fast as possible, technically interesting, but might be
absurdly boring to watch. We don't want to mix those up or substitute one for another, because these 2 are independent and interest people in their own ways. We as a site want to showcase both ways of superhuman play.
Oh yeah, and the branch name itself. Glitched is used since 2005, it was introduced with Zelda games. There are 54 published submissions for that branch. So this is traditional. It's not as traditional as any% or 100%, since those root back into console speedrunning, and you can't skip to game end consistently on console (only with some side abuse, like savestate+reset, which seems to have separate branches on SDA). But the term is well-known.
Why some certain term for all "game end by soft-hacking", not mentioning the exact glitch that causes it? Because once you have a good bunch of things having something similar but applied the hard way, you can abstract it and apply the soft way (optimization). Why name out each when they really have something common? Moreover, when naming the exact glitch, you easily stop having the clear branch. It may be a chain of 10 obsoleting publications each abusing a different glitch to end the game. So what, have 10 branch names? Having 1 branch for all of them is clear and consistent within that game, and consistent to the whole site's branching.