This propabaly differs from one company to another but what I explain to my users is this:
Versions have to do with physical file management & capture moments in time similar to incremental "saves" when you are at work-in progress. The vault creates a new version of a file & archives the previous version every time you check out & check in. Each "version" of a file in the file store is a separate file.
Revisions are more business process related and have to do with the release states of a file.
Example: I have to change PART A which was last released @ Rev C (in vault terms it may show as version 12). I will check it out of vault for edit, then check it back in for review by an engineer, it will show as version 13. The engineers makes further changes etc. When everyone is ready for approval, the file would be checked out to get its properties (sign offs & dates) edited & checked back in as PART A vault may show it as Version 20 by now, and in the comments field, we note Released @ Rev D.
Vault does a comparision between the file in the file store & what is on your local. It does not know anything about what has changed, only that there has been a change. Vault cannot recognize that you have changed the release state of a file from Work-in Progress to Released which in most companies constitutes an actual Revision. That is one reason that they have added the ability to apply Stamps in Vault.
The business definition of files and their Releases & Reslease states is part of what ProductStream is intended to handle.