basically, yeah. internet is network of computers spanning all earth. intranet is smaller network of computers. intranet is often more private network under more centralized control of someone, with limited access from outside, that can be operated for example by some corporation or university, accessible only for employers or students (possibly using vpn to remotely connect to the network).

www. is the name of the service - http is a protocol it uses.

e-mail is the name of service - to access it, lot of people use http protocol if you use webmail, or imap or pop3 protocol if you use some dedicated client (like thunderbird, outlook, or others). smtp protocol is used to send the message to another mail server (you may have also been asked to configure it when manually configuring some dedicated e-mail client).

ftp, ssh, bittorrent,VOIP telephony using SIP protocol, IRC are other useful services. all these services can be run on network of any size, internet or intranet.

for example majority of modern doorbell systems are running on sip protocol and they are basically small VOIP phones running primarilly on a limited intranet in one specific building, but, due to nature of what they are, they often have an option to forward that “call” into any other telephone number in case no one picks it up at home.

small web-developers routinely run their own web-server of their own desktop, which may only be accessible locally, from that one computer or their small home network, to test the web pages they are developing. whether it is still world WIDE web is funny academical question then, because that web is not very wide in such case.