In practice
Claude Code, Cursor, Claude, ChatGPT and several editors can act as clients. They discover what a server offers and call its tools during a session.
“Client” and “host” are sometimes used for the same thing. When people separate them, the host is the app you use and the client is its connection to 1 server.
The client isn't the model. The model chooses a tool. The client makes the call and returns the result.
Why it matters for product builders
Client support decides who can reach a server. If it works in only 1 editor, everyone else is excluded.