They're the same thing, isn't it? Except that with add the "at constant temperature" addendum, you're just making explicit the other variable(s) that can potentially be varied. Without it, it just means all other variables, whatever they may be, are constant.

But if something depended on both temperature and some other quantity X, and you said "partial derivative of pressure with respect to volume at constant temperature," that would be sort-of misleading because you're only exlicitly mentioning one of the other two variables - rather, you should say "at constant temperature and X" or not mention either of them.