The article "What Is Difference Between a Beamer & a Multimedia Projector?" by Sarah Clark explains it.
"Beamer" is a word used in European countries that is synonymous with
"projector." A European beamer has the same standard equipment and
serves the same purposes as an American [multimedia] projector.
It also states:
There is no difference between a beamer and a multimedia projector,
except for their names. Of course, there are differences between the
functions and capabilities of all projectors, but those differences
are determined by brand and style.
So, the word beamer is European English and refers specifically to a multimedia projector, not just any projector. Americans probably won't know what you mean if you use "beamer" to mean that unless you're standing right in front of one and are pointing at it while calling it that.
Actually, the word I use and everyone I've heard use, like at the high school 🏫 (American ) where I work, is "proxima," which I think came from a name brand, kind of like "kleenex." I say "proxima" to mean a projector that hooks up to a computer as opposed to saying "projector" because "projector" is taken as meaning a film projector, so if I ask the A/V Department to bring me a "projector" third period, they'll bring me a film projector 📽️. I have to ask for a "proxima" if I want them to bring me a multimedia projector. But maybe that's just where I am, jargon at my work, because it's not like I talk about this stuff outside of work to know what other people call it. I wonder what they'd do if I asked them for a "beamer"?😉