Document Centre is the main site repository where you would start authoring (think about it as a kindergaten or school) you create, collaborate, update etc. (lots of reads and writes)
Now Records Centre is your graveyard, you send the document there, there will be no more updates on it (so possibly more reads than writes, but experience shows me that there are writes, most of reads are from indexing engine ;)
For the other question what makes one or the other better from the Document Library: Nothing. It is different level. Document and Record Centers are site collections (Parent) that can contain multiple Document/Record Libraries (Children).
Down the line, there is really not much difference between 'Records Center' library and document library. The main one is that the document parser is turned off and you loose some of the functionalities like property promotion from Word to SP column, but as this is a 'Record' such, changes should not happen anyway. You would put there sign contracts with Employees, Customers etc. those documents that by regulation (or other driver) you are bound to keep for certain period of time before you can destroy them.