What's the difference between Texas Hold'em and poker?

Alright, so I was at a gathering the other night, and someone said, "You play poker? Oh, you mean Texas Hold'em?" And I just kinda nodded along, but it got me thinking—what’s the actual difference?

I always thought Texas Hold'em is poker, but then you hear about Omaha, Seven Card Stud, Five Card Draw, and now I’m questioning everything. Like, is poker just the umbrella term for all these, or is Texas Holdem its own beast entirely?

If I know how to play Holdem, does that mean I can walk into any poker game and not look like a total amateur, or are there some massive rule changes I need to know?

Help me out here before I embarrass myself next time someone brings it up.
 
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