Remote communication between clients

Still not clear to me what 'client' means in this context. Are 'clients' connected to a server? Are you using a web service, normal sockets, carrier pigeon ... what is the message in question being sent over?

You need to choose some sort of transport. Assuming internet communication, that will be TCP/IP or a protocol on top of TCP/IP like HTTP. Client-to-client (or peer-to-peer which is probably what you mean) means one or all peers need to be able to listen for connections, effectively making every "client" a "server" as well. That brings in administration issues - many computers aren't set up to allow incoming connections by default, and many network admins won't allow it. Do you really want your users to have to configure firewalls and port forwarding? This needs to be taken into consideration.

Since most machines are configured to allow outbound connections (like accessing the web)I personally use a server (usually using HTTP protocol), which acts as a relay server. Clients don't directly connect peer to peer, but instead only connect to the server. The server relays messages (or media streams) on to the recipient peer(s). This way the only administration issues are on the server.