ITSPs – what they do
An Internet Telephony Service Provider brings to its customers SIP trunking connections that allow for outbound and inbound calls to/from the Public Switched Telephone Network (PSTN), to/from the Public Land Mobile Network (PLMN), and to/from other SIP users.
ITSPs don't need to own a physical Internet backbone, nor the "last mile" of cables going from the backbone to their customers' premises. ITSPs connect to the public Internet and operate their own SIP servers and (optionally) their own gateways from SIP to PSTN (from now on we'll write only PSTN, for brevity's sake, meaning both PSTN and PLMN).
ITSP business is to sell minutes of PSTN communication to their SIP end users: Both communication coming from PSTN (a caller from PSTN wants to reach a number connected to the SIP device of an ITSP's customer) and communication going to PSTN (ITSP's customer from his/her SIP device wants to call a number connected to the PSTN).
In the real world, much SIP to SIP communication...