Regarding the underwear thing, that's a fairly common trope in anime - girls in a high school setting are expected to wear plain panties, but then there's one girl who wears something unexpectedly risque, like frilly black or red panties ("adult lingerie"). In this case, I guess she doesn't necessarily wear it to school but she has some at home. Maybe it's more surprising because she's a bit of a tomboy by this time.
Seconding this interpretation. My vote is for Risqué Panties (or Risque Panties). Tifa is... a bit sexually repressed, and she's 16 at the time, so I think it's more likely she'd have this kind of secret rather than being embarrassed by "Frilly Knickers" or "Fancy Underwear".Edit: Sorry if this is backseat translation but I did some digging --
according to the JP text dump the line is:
『ちょっと背のびパンツ』を手にいれた!
( chotto se nobi pantsu ) wo teni ireta !
This can be translated various ways.
ちょっと: Small, little, or "a bit".
背: Back/spine, sometimes disobey/rebel.
のび: Grow, stretching, extending.
背のび: Overstretching oneself, stretching your back to make yourself seem taller.
I like the reading that the panties were "a little 背のび", implying (Cloud thought/suggested) that Tifa was trying a little too hard to seem grown-up. In this light, my suggestion of "Risqué Panties" doesn't really work, especially considering
the International Version graphic is anything but risqué, but I also don't think "Frilly Knickers" captures the meaning either. The scene is being told through Cloud's perspective and, well, intended to embarrass Tifa, so it's pretty important to the joke to directly portray his thought that they were age-inappropriate (also because Cloud is a bit of a dork). "Adult Panties" might work, "Grown-Up Panties" might work better (because only children say "grown-up"). "Fancy Underwear" is definitely pretty good, because coming from a guy, a thing being "fancy" has a sort of judgmental tone (e.g. "Tifa thinks these 'fancy' panties will make her seem more grown-up").