That term almost exclusively refers to thermonuclear weapons.

The amazing Ukrainians created what's basically a fuel-air-bomb often referred to as a thermobaric weapon. By spreading the hydrogen out you get a larger bang because the mix reaches a better mixture between the air (oxidizer) and fuel (hydrogen) powering the explosion. It's damn nifty and props to them, but it's not a hydrogen bomb in the conventionally used sense of the word.

I really dislike the term hydrogen bomb because I don't want anyone, anywhere to confuse the terminology and give RU any excuses to escalate from conventional weapons, which probably sounds like an overreaction but if you see the shit the russians use to justify their bullshit...

See: russian accusations of use of chemical weapons while they're being accused by ukraine of using chemical weapons. Don't give them loaded rhetorical talking points.

Personally, I think that "hydrogen bomb" is a worse name for the fission/fusion bomb than for this one. I mean, it is what it is because the name has meant the fission/fusion bomb since it first became a thing, but it was either a bad naming or the name was selected because it was deliberately misleading (cold war and all).

500 lbs is the standard size bomb that US fighter aircraft carry. Some of them can carry up to 2500 lb bombs, but lose their stealth capabilities because the bomb is outside the airframe.