The difference between nuclear waste and nuclear weapons?

The exact contents of radioactive waste from a nuclear power plant and radioactive fallout from a nuclear weapon can vary widely but are likely to be similar in their primary isotopes.

The major difference between the radioactive waste from a nuclear power plant and radioactive fallout from a nuclear weapon is that the waste is normally contained and will not enter the environment (unless an accident happens) while the fallout is dispersed into the environment and is carried by the wind (sometimes all the way around the world multiple times).