America is a democracy AND it's a republic AND a bunch of other stuff.
The full description is that America is a Federal Constitutional Representative Democratic Republic.
And yes, saying it’s not a democracy infuriates me as well, because it’s being used to justify a whole lot of undemocratic shenanigans.
Also: continents are bullshit.
Also also: America is the United States of America in the English-speaking world.
As an Australian English speaker, I will normally call it “the US”-the only time I ever call it “America” is when speaking to our 7 year old, because I know she knows what “America” means but I worry “the US” might confuse her; but with older children (such as our 12 year old) and with adults I say “the US”, because calling it “America” feels incorrect to me. In everyday speech, “the US” is (in my experience) more common than “America”, although both are understood as referring to the country; for the continent I use the plural (“the Americas”) to avoid the risk of confusion.
"A cat is not a pet, it's a feline."
Things can be multiple things at once. The US are a republic and a democracy. Republic = not a kingdom, democracy = power to the people. Close but not exact synonyms.