i don't think there is a strict definition for the term "client". the client is usually referred to software that is capable of some pretty basic functionality including private/public key and address generation, transaction signing and connecting to bitcoin network (in one way or another).
with that definition a client can include full nodes, pruned nodes, SPV nodes and mobile wallets. the only thing that may not fall in a "client" category is web wallets and custodial wallets.

for more info an a list: https://en.bitcoin.it/wiki/Clients