You're talking tactical and strategic weapons.

Tactical would be used in the battlefield in the form of smaller rockets or freefall bombs under military situations.

Strategic weapons would usually be a higher yield and are made to threaten a country's population, infrastructure and military; or to cripple the country's ability to wage war.

ICBMs are tactical nuclear weapons. The B61 bomb is a tactical weapon though it does serve a dual role as a strategic weapon.

A nuclear bomb is any bomb with any nuclear or atomic material inside it, while a plutonium bomb is a specific type of nuclear bomb. Plutonium could be the nuclear material inside the bomb, and if it is, it's a plutonium bomb.

the hydrogen bomb, is a nuclear bomb

A bomb can be either conventional or nuclear.

Do you mean types? For instance like the W80 warhead, B61 bomb, W88 warhead, B83 bomb...

Or do you mean types? Spherical Implosion Weapon? Gun-Type weapon? Linear Implosion weapon?

Or do you mean the code names given to some of them like the "Davey Crockett" or "Little Boy" or "Fat Man" or "Swan"