Daemon is the unix term for an application running in background.

On servers this is the normal case for all applications, so you can just call it a server software.

On desktops, mobile or embedded platforms such daemons frequently act like a server to the user interfaces running on the same device, but may interact with remote entities over the Internet as a client or as a P2P node.

psyced can be operated in such a way. Saikound is even intended to be operated this way.