Database Install Issue
Have never encountered anything remotely like this and suspect something has been lost in translation. I will of course apply the usual caveat for licensing questions, "don't take anything you read here as gospel, check it with your licensing partner, and Microsoft, and call both back to speak to a different individual. There's a good chance you'll get a different answer the second time around".

You get a key, you install the software. Any CPU limitation is a product of the physical environment or version of SQL Server. For standard edition that is:


  Limited to lesser of 4 Sockets or 16 cores [source]


A volume license agreement is essentially a discount pricing arrangement, it does not involve a different installation, key distribution policy or CPU utilisation limitation:


  If you plan to buy five or more software licenses, Microsoft offers
  price advantages for volume purchasing. Discover how Microsoft Volume
  Licensing can help your organisation realise its goals and find out
  what customers and analysts have to say about it.
  [source]


Licensing is always complex. Microsoft licensing is at least as complex as other vendors. Unfortunately, my experience has been that they have not yet mastered the art of training their own, or their resellers employees about license models. 

There is much fun to be had by locking a Microsoft licensing specialist in a room with a reseller specialist and watching them argue about the finer points of SQL Server or MSDN license arrangements. If you think SQL Server is a minefield, try MSDN.

NB: The "helpful" diagram at the top of the article explaining edition compute capacity limits neatly demonstrates why folk lose their way.