The original and complete form is "che cosa". Then, in the evolution of the language people and also notorious writers started shortening to only che or only cosa, so today they are considered also both correct and having the same meaning - I am obviously referring only to the context where it is direct or indirect interrogative sentence (what?/tell me what). Che fai oggi? Can be replaced by Cosa fai oggi? Che bello! Can not be replaced by Cosa bello!(wrong) Dimmi che compri oggi = dimmi cosa compri oggi = dimmi che cosa compri oggi

Hi, if you mean these words for "what" there are no differences You can use them at the same way. "Cosa hai studiato per oggi" --> "what have you studied for today" "Che hai studiato per oggi" --> "what have you studied for today"