I am very confused over usage of PSTN and VOIP-SIP please clarify it.
The public switched telephone network (PSTN) is where all the numbers of the world lives, You can connect to the PSTN using ITSP(internet service provider a.k.a SIP or IAX Trunk) or using Analog lines(the old ones lines with copper) or Digital lines like E1 or T1s.
Asterisk is a suite that allows you to connect your PBAX to the PSTN using one or more or all of the technologies above, then since Asterisk is network based it converts your calls or your service in a VoIP(Voice over IP) service. Even if you don’t connect to the PSTN you are giving VoIP services to your internal users.
Google can clarify better your doubt.