Is there any difference in the radioactive fallout from fission bombs or fusion bombs?
Yes.
Fusion bombs can be much,much worse.
They can be many times more powerful, and can be made extremely “dirty” by using a U-238 tamper. A “clean” h-bomb is not going to be as bad as an A-bomb of the same yield, but it’s still going to be bad.
H bomb is a bit of a misnomber. Its A+H. Set off a small fission bomb right next to the hydrogen,to trigger the fusion of the Hydrogen. Fusion produces radioactive fallout on its own (especially as the hydrogen is surrounded by uranium- uranium is used for its density.) so there can be more radioactive fallout (measuring the sum of radioactive particles … not the total mass of fall out.) from the hydrogen bomb than the fission bomb would cause on its own.
Fallout; increasing your risk of dying from cancer in a few decades.
IIRC, outside of deliberately salted weapons, the only one where you need to worry about fallout bring lethal in hours or days are smaller sub-KT types, for every other type if you are close enough for prompt radiation or fallout to be lethal, you are close enough for the blast and thermal pulse to do kill you anyway.
Interestingly I read somewhere that in one respect its better to be targeted by a large multi-megaton weapon than a smaller kiloton yield weapon, this is that the ‘rise time’ to reach maximum temperature is far quicker for a smaller than a larger device so if caught out in the open you might have more time to reach shelter in the latter case.