Xwindows is a server in the same sense that a network printer (or print server) is a server: it sits there waiting to receive network connections from clients,

Xwindows is a server in the same sense that a network printer (or print server) is a server: it sits there waiting to receive network connections from clients, and it allows whoever connects to do stuff which is tangible to the user. The fact that you're interacting with it makes it also feel like a kind of client. But technically, the clients are asking X to allow them interact with you. Though one of the things you may do with X is control launcher software that ends up starting more clients which interact with you through X.