I was working with some ITIL-type concepts before ITIL was well known. Pretty much all of us are, although many of us do not know it. I think of ITIL as a framework to not forget about some of the stuff that should be considered as we manage our IT and ops stuff. If you get ITIL training, part of it is about using terminology differently - we all know that people using the same word to mean different things can lead to confusion, especially in the tech. industry, so this is important. The other part is getting a list of all the stuff you should pay attention to - and it is meant to be a complete list.
CMDB is an inventory of stuff. A good inventory. For example - I have a list of all of my servers, and what they are for. Information about when they were deployed, and what their service contract is, if any, is in there. Then, instead of checking all the servers, we check the CMDB. It is just the database of record for what I choose to put there. It can be in several places - we use a separate database to track hardware problems. In the grand scheme of things, it is part of the CMDB too - the database of record of what is what.
