Yes, you are correct (I speak Dutch, not German, but they are very close).
In Dutch we use a lot of English words: Computer, keyboard, ... . So when I hear an English sounding 'beamer', I think it's English :).
We basically use 'projector' for anything from slide to video projector. But it seems the digital age introduce a new word 'beamer' in our language (and German), that didn't happen in English.
Beamer is pronounced just like bimmer, which to most in the US (or at least my part of it) is just a nickname for BMW cars. That said, beamer as the word for projector has that German feel of being “obvious” to it, and is neat.
In Dutch we use a lot of English words: Computer, keyboard, ... . So when I hear an English sounding 'beamer', I think it's English :).
We basically use 'projector' for anything from slide to video projector. But it seems the digital age introduce a new word 'beamer' in our language (and German), that didn't happen in English.