This sounds like a better question for your licensing provider than a random forum post, but I can try to help here.
Best I can tell, there is no difference between the two. How I came to this conclusion - I have downloaded the installer from my visual studio subscription and entered the license key provided by IT (who manages the purchases of the licenses) and my installs have always gone smoothly. Visual studio doesn't even give you the option to download a "Server/CAL" version or a "Core" version, just an EXE or OTH.
If you wish to verify it though, I would say download the SERVER/CAL version and the Core version then use an MD5 hashing tool to generate the MD5 hash on it and if the 2 MD5 match, they are the same file. If they don't match, they are different files.
But again, I would start by asking your license provider as they are the best resource for this type of question.
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!