In a client-server model, the server serves services to the client.

The client/server model is a model where there are two distinct parties: One party provides services, the other uses them. It's the opposite of a peer-to-peer model, the parties are both server and client. For example in the Bitcoin peer to peer network, the programs on the user's computer acts both as a server (it uploads blocks and confirms transactions) and as a client (it downloads blocks from others and asks to confirm transactions).

Surfing the web is a good example of a client/server model: The websites are served by the servers, and the browser acts as client (it uses the received data).