There are 2 major differences.

1. Technical
2. Licensing

Technical, there are 3 major differences:

First and foremost, Community doesn't have TFS support.
You'll just have to use git (arguable whether this constitutes a disadvantage or whether this actually is a good thing).
Note: This is what MS wrote. Actually, you can check-in&out with TFS as normal, if you have a TFS server in the network. You just cannot use Visual Studio as TFS SERVER.

Second, VS Community is severely limited in its testing capability.
Only unit tests. No Performance tests, no load tests, no performance profiling.

Third, VS Community's ability to create Virtual Environments has been severely cut.

On the other hand, syntax highlighting, IntelliSense, Step-Through debugging, GoTo-Definition, Git-Integration and Build/Publish are really all the features I need, and I guess that applies to a lot of developers.

For all other things, there are tools that do the same job faster, better and cheaper.

If you, like me, anyway use git, do unit testing with NUnit, and use Java-Tools to do Load-Testing on Linux plus TeamCity for CI, VS Community is more than sufficient, technically speaking.

Licensing:

A) If you're an individual developer (no enterprise, no organization), no difference (AFAIK), you can use CommunityEdition like you'd use the paid edition (as long as you don't do subcontracting)
B) You can use CommunityEdition freely for OpenSource (OSI) projects
C) If you're an educational insitution, you can use CommunityEdition freely (for education/classroom use)
D) If you're an enterprise with 250 PCs or users or more than one million US dollars in revenue (including subsidiaries), you are NOT ALLOWED to use CommunityEdition.
E) If you're not an enterprise as defined above, and don't do OSI or education, but are an "enterprise"/organization, with 5 or less concurrent (VS) developers, you can use VS Community freely (but only if you're the owner of the software and sell it, not if you're a subcontractor creating software for a larger enterprise, software which in the end the enterprise will own), otherwise you need a paid edition.

The above does not consitute legal advice.
See also:
https://softwareengineering.stackexchange.com/questions/262916/understanding-visual-studio-community-edition-license

I wonder who is in charge of naming and versioning over there!

Naming is a marketing thing. Versioning is a technical thing. Don't confuse the two.