[marifjeren]

Typically you run both the client program and the server program on your computer during development. Even though they're running on the same machine they can talk with one another using http as if they were both on the world wide web.

Then you deploy the server program, and then you deploy the client program, to another machine, or machines, where they continue to talk to one another over http, maybe over the public Internet or maybe not.

Deploying can mean any one of umpteen possible things. In general, you (use automations that) copy your programs over to dedicated machines that then run your programs.