yeah it kinda drives me up the wall too. goth dates back way before the 2000s. emo started getting big in the 00s (at least in the way it's come back, but 'emo' existed back in the 90s in a way different form) so with that i kind of understand referencing it being from the time period. but y2k and frutiger aero are SO different.
there's related style factors between the two, but they're easy to distinguish if you know what's up. i kind of blame the blurring of them on the "tiktokification" of aesthetics. they're often presented too close together to allow people to actually define what they are in their own minds if they're not branching out past a surface level. no shade at people who do that btw; some folks only wanna engage with stuff on that kind of level and that's fine! but it def leads to frustration for me sometimes when you wanna see people 'get' it y'know?
for anyone seeing this who feels unsure, i recommend evan collins' are.na pages on y2k and frutiger aero respectively to get a gallery look at the differences between them.
his page overall has a great collection of all different kinds of aesthetics! it helped me put a name to what he calls "post-grunge-maximalism" which i have a lot of nostalgia for, but never could have defined beyond a vague idea.