Basically the answer to everything you asked is "yes"
You might not want to go any further into it though since it gets pretty messed up.
The physical routing type of address for my machine is 63.199.8.158. You can see my default web page by putting
http://63.199.8.158 into a browser. You can send me email to gandalf@[63.199.8.158]
That also translates to a long number of 1070008478. You can go to
http://1070008478 and send me email at gandalf@[1070008478]
It was originally adsl-63-199-8-158.dsl.snfc21.pacbell.net and that works as
http://adsl-63-199-8-158.dsl.snfc21.pacbell.net and as
gandalf@adsl-63-199-8-158.dsl.snfc21.pacbell.net also altho the web page is just a place holder.
I have
www.dom2minions.com,
www.alt-hacker.org,
www.sdmud.org,
www.techno-mage.com, and
www.shadowdale.org (some others I forget) pointed to that machine. If you type those into a browser it looks up the DNS and gets an address of 63.199.8.158 (my web server sees the incoming address and shows the correct page). And you can send me email to gandalf@ any of those. A domain name is portable, the IP pretty much is not. Think of it as the difference between Gandalf Parker living at 1214 Balsam Way. The name might change but the physical address doesnt move around easily.
Now the fun part, reverse lookup. A whole different set of servers handle the IP to name lookup. There can be many names pointed to an IP but an IP can only have one name associated with it so a reverse lookup of my IP says that 63.199.8.158 is actually alt-hacker.org
Want more fun? Mac addresses. More fun? IPV6. More fun? DHCP
By the way, dont look too hard for logic in all of this. The growth of the Internet had less in common with engineering,
planning and design. And more in common with chaos theory, big bang expanding universe, and the theory of evolution.