They are different names -- essentially (hypothetical names used here):
domain name registrar: BIGBULKCHEAPHOST.COM name server: QQ1.SERVERNAME.COM
registrar for the above name server: ANOTHERCOMPANY.COM
So to which registrar do I submit the DMCA take-down notice? The second one would seem to make more sense, since they have control over the actual server that stores the infringing material (web page). Right?
I'm sorry if I sound naive, but I just don't know how the domain registration business works. It looks like several different parties in a chain each take a little piece of the action. I find it very confusing.