RFC 3261 defines these server elements:
A proxy server "is an intermediary entity that acts as both a server and a client for the purpose of making requests on behalf of other clients. A proxy server primarily plays the role of routing, which means its job is to ensure that a request is sent to another entity "closer" to the targeted user. Proxies are also useful for enforcing policy (for example, making sure a user is allowed to make a call). A proxy interprets, and, if necessary, rewrites specific parts of a request message before forwarding it."
"A registrar is a server that accepts REGISTER requests and places the information it receives in those requests into the location service for the domain it handles."
"A redirect server is a user agent server that generates 3xx responses to requests it receives, directing the client to contact an alternate set of URIs.The redirect server allows SIP Proxy Servers to direct SIP session invitations to external domains."
The RFC specifies: "It is an important concept that the distinction between types of SIP servers is logical, not physical."
Other SIP related network elements are
Session border controllers (SBC), they serve as middle boxes between UA and SIP server for various types of functions, including network topology hiding, and assistance in NAT traversal.
Various types of gateways at the edge between a SIP network and other networks (as a phone network)
Another important element is the SIP Location Server. It provides information about a caller's possible locations to redirect and proxy servers. Also, it may be co-located with other SIP servers.
This is a quick overview, I will add a more detailed reference later.