I think the sentence structures are as follows:
- "the Germany national team" [definite article], [adjectival noun], [adjective],[noun]
- "the German national team" [definite article], [adjective], [adjective],[noun]
So the first is the national team of the country Germany. The second is the national team which is German. It's just in 99% of cases, they amount to the same entity.
For a clearer example (where there's less alignment), in football (soccer):
- there are four teams that you could technically refer to as "the British national team" — i.e. one of the teams of England, Scotland, Wales or Northern Ireland
- but "the Britain national team" doesn't exist
- there is only one "England national team"
The above example is a bit of a stretch, as you'd be unlikely to use "British" as per the first bullet, because it would be too confusing, though the England national team is technically British.
Another place you see a similar (and more useful) distinction, also in sports reporting, is with individual players — if Messi plays for Barcelona, he could be described as "the Argentine international", even if he gets dropped from his national team, as he is an international player in Spain. If you call him "the Argentina player" however, it suggests that he's a player currently on the "Argentina national team".