Your computer + other computers at home connect to a router to form a local network.

Your router is connected to a modem, which connects your local network to the telephone infrastructure.

Thus we can send messages from our network to other networks through ISPs which manage their own fleet of routers that connect to other ISP routers

Your network ID is called an IP address

A domain name maps a human readable address to your IP address (A Record)

The internet is the INFRASTRUCTURE. The web is a service built on top of the infrastructure.

References

https://developer.mozilla.org/en-US/docs/Learn/Common_questions/How_does_the_Internet_work