I am not a native speaker. I found that it is easier for me to say this to my daughter when we go out "Sweetie, please put on your top / bottoms" than "Sweetie, please put on your Tshirt / shirt / tank top / pants / shorts..." because I don't have to think what specific kinds of tops and bottoms she should put on & it is up to her to choose what to put on.
are "put on your top / bottoms" more common than "put on your Tshirt / shirt / tank top / pants / shorts ..." in English in casual daily situations?
In Ngram, "put on your shirt" is much more common than "put on your top"