Are all grips with the same size the same size? for example, is a size 3 grip in a Head racquet exactly the same size as a size 3 wilson racquet? Sounds lieka silly question but if I try a size 3 grip in the shop with just the normal grip it feels too small but I have a size 3 Head racquet with a thin overgrip on at home and it feels the perfect size. But size 5 feels too big.

Please advise on what to do?