I understand that in French we refer to floors as "rez-de-chaussée, premier étage" etc., but if you want to tell someone how many floors a building has, does this still hold? I.e. if it only has the ground floor, does it have aucun étage, or if the floor highest up is the "deuxième étage," does it have deux étages? I feel like that's how I learned it in school but it's been a while so I wanted to double check
You have it right: according to the TLFi, étage seems to refer to the space between two floors, so you'd need indeed two floors to make un étage.
A house with only the ground floor has "aucun étage", it is "de plain-pied".
A house with three floors, so the rez-de-chaussée + le premier étage + le deuxième étage has deux étages. The ground floor is implicit. This same house has trois niveaux (levels, floors).
Note that historically, both versions seem to be correct:
Le premier étage, anciennt. et encore au Canada, le rez-de-chaussée ; auj., l'étage carré situé au-dessus du rez-de-chaussée ou de l'entresol.
Disclaimer after reading some comments: the following statement is based on a few buildings I saw, which doesn't mean it's a rule, just that it can happen.
In some buildings and industrial constructions, the actual numbering may vary (probably depending on how it was designed). I have seen the rez-de-chaussée being numbered 1 and the following floors 2,3,4, etc. It's absolutely not the most common situation, though.