Web-based apps are a form of client Server, but not all client server apps are web based.
Web based uses standard internet protocols, HTML, and so on. Client server apps can use those protocols, but they don't necessarily have to.
Plus, client server usually implies a bit more activity at the client, where you have more of an application there, one which gets the data it works with from a server but does a fair amount of work at the client.
A web app leans more toward the client merely viewing the presentation that has been created at the server.