Sure, I am aware of this difference but really don't understand why SDLX can't use the same translation memory to check terminology consistency.
Well, this is because a TM is not meant for managing terminology (individual words or phrases) but for saving complete sentences rather than individual words.
This isn't special to SDLX but is the same with all Translation Memory tools I know. They all have separate tools for terminology management. If you want to check the terminology once you have completed the translation, you either need a terminology database from the start or you need to create one while you're translating the text.
A friend of mine just exported the mdb file to txt, and then imported it to a new tdb file. To do this, one have to own SDL Professional.
That's what I would have suggested. Please note though that you don't need SDLX Professional for this, the Freelance version will do (it's not possible to do this with the Lite version though).
However, if your TM contains sentences, it still won't be very helpful for checking the terminology even if you convert it into a .tdb file.