Re: I'm confused
Although DNS provides a mapping from a domain name to an IP address and you then contact that IP address, the IP address in itself doe not identify the domain name or website you are contacting. Lots of website run on shared servers so a log of IP addresses accessed doesn't reveal a great deal about the sites you're visiting.
When you posted here the domain name forums.theregister.co.uk returned an IP address, but checking that IP address just reveals that currently El'Reg seems to be hosted by Cloudflare.
If you are using HTTP then of course the website you want is going to be in the packets you send to that address, so the ISP / BigBrother / monitoring service can see them then. If you are using HTTPS then the negotiation over the certificate is in plain text, but even this doesn't need to reveal the name of the site you are visiting as one certificate can cover multiple websites.