Wow! That is super confusing. What I think you are asking is about why domain name registering and website hosting can't be separate. Well they can be separate. You can go to google and search for domain name registration and find tons of sites that do just that. I highly recommend
Go Daddy. They have very a very good support and very cheap (if not the cheapest) prices. I have a domain name with them and they are great! All domain registrants have a nameserver setting. The nameserver is what tells the webrowser where to go to (ie the ip of the website). You can either use the registrar's nameserver or go with a site like
ZoneEdit. Either way you can then point the domain name to a website hosted by sites like yahoo or netfirms or you can point it to your home computer's ip address and host your own server. If you choose the 2nd option you will need a static ip unless you want to get a Dynamic IP client which can automatically update the nameserver with your new ip whenever it changes. I have this setup and it works pretty well.
DSL/Cable Webserver is an awesome resource that can give you lots more info on all of this. Well I hope I answered your question. If I didn't then I just wasted 10 minutes of my life writing this. Oh well.
