Do nuclear bombs come in different sizes or is there a "standard" one-size-fits-all that all countries have?

Different. The fission bombs that flattened Hiroshima and Nagasaki were a fraction of the yield of an H-bomb - in fact, bigger bombs than those are used as DETONATORS in an H-bomb.
The "little boy" and "fat man" fission bombs used in World War Two had nominal yields of 13 and 20 kilotonnes respectively (the same explosive yield as 13000 and 20000 metric tons of TNT). The biggest bombs in active service in the US are the B83 fusion bombs with a yield of 1.2 megatonnes, the biggest US test was the Castle Bravo device (15 megatonnes), the biggest ever built by the US (but never exploded) was the Mark 41 with a 25 mt nominal yield.
The biggest bomb ever tested was the USSR Tsar Bomba, with a yield of 50mt - it was initially designed to have a nominal yield of twice that but the Soviets weren't sure how much damage a bomb of that size could actually do to the Earth's crust, so they built it with a lead tamper rather than a depleted uranium one, thus halving the yield.
North Korea is not believed to have any fusion weapons, the biggest fission bomb they have yet tested had a yield of between 15-25kt, comparable with the Nagasaki bomb.