Somehow, I feel clear about definitions of daemon and server after learn a little bit about X11. So, I would like to have verification to my definitions as below.
Daemon is a process that is not associated with any terminal (has no controlling terminal).
Server is a process usually but not necessarily a daemon. Examples of daemon server are sshd and sftpd. Example of non-daemon server is X11. X11 has terminal associated with it, usually tty7.
The terms "daemon" and "server" can mostly be used interchangeably for any process that runs in the background and that provides a service.
A daemon, as you point out, is usually not associated with a TTY, but this goes for most servers too. Such a technical detail is minor since there is no definition that provides a clear distinction between the two terms that is applicable to the way the terms are used in everyday language.
Furthermore, a daemon acts like server when a client accesses its services (in the server-client paradigm). Again, the term "server" and "daemon" are interchangeable about the same entity.
The term "server" is also associated with a host (machine) that provides a service, such as a file server (which may be running an NFS daemon).
