I'm asking because I didn't find any answer on the Internet, even on the sites dedicated to these sports.
Both badminton and squash are played on similar surfaces and both require quick changes of direction. They both require shoes with flexible, grippy and non-marking soles. Shoes marketed as for badminton shoes might be lighter as there is more focus on jumping than in squash, but the variation is minimal and mostly just marketing/labelling.
(Tennis shoes on the other hand are usually intended for outdoor use and will have different characteristics)
I know plenty of people who play badminton at local league level using shoes marketed as "squash shoes". No doubt some squash players play in shoes primarily intended for badminton too.
Whichever sport you play, you should probably try on shoes marked as for badminton and those marked as for squash to see which is more comfortable for you. This is far more important than having a label which matches your sport.