Asterisk supports many telephony protocols, including SIP and IAX. SIP is the most popular open standard (Skype is by far the most popular VoIP protocol, but it's closed and proprietary), and does quite a lot more than "just" VoIP (it's a Session Initiation Protocol for more than just global addressing and realtime duplex audio). It's the most well supported by TSPs (Telephony Service Providers), including lots (probably most) voice switching equipment, including the really big stuff.
IAX, though, is an Asterisk-specific protocol. It's open and standardized (and nonproprietary: free in every way except maybe trademark), but it's really the Inter-Asterisk eXchange protocol, originally designed for server-to-server Asterisk networks. But it has an advantage over SIP in that it uses a single socket for a session, rather than 2+ for SIP, and has other characteristics that make it work better over NAT and some other hacky network configs (including just plain firewalls). It's supported by clients, not just Asterisk servers, and even some HW, like hardphones and ATAs. Plenty of TSPs support connecting by IAX, especially if they're exposing Asterisk servers as gateways to their services, but it's nowhere near as popular as is SIP.
Whichever one you use, you've got to config Asterisk to use it specifically, even if just in order of preference in a list with SIP. And the peer to which you connect has to support the protocol you specified.