The two bombs used in WWII were "atomic" . Read any book or watch any film thats what they are called. Calling them nukes is like calling them H- bombs. They are the same, but at the same different.
"The original atomic bomb used nuclear fission, in which big atoms (uranium or plutonium) were split into littler ones in a chain reaction, releasing vast amounts of energy. The hydrogen bomb employs nuclear fusion, in which little atoms (various forms of hydrogen) fuse together to make bigger ones (helium), essentially the same process that occurs in the sun."