Difference between Ciao REST server and Ciao REST connector and when to use each or the other
I don't know about "Ciao" but generally a rest server answers requests from a client that is connecting via a rest connector.
You client will use POST, GET, PUT, etc. to ask the server to provide a service.  This could be as simple as "GET .\index.htm" or more likely posting information to be stored in a database.

The server will sit waiting for these requests and will have handling routines for each specific request and might supply a response.