You might think of the explosive part of a nuclear weapon as the “weapon” or “bomb,” but in the technical literature it has its own kind of amusingly euphemistic name: the “physics package.” This is the part of the bomb where the “physics” happens — which is to say, where the atoms undergo fission and/or fusion and release energy measured in the tons of TNT equivalent.
Drawing a line between that part of the weapon and the rest of it is, of course, a little arbitrary. External fuzes and bomb fins are not usually considered part of the physics package (the fuzes are part of the “arming, fuzing, and firing” system, in today’s parlance), but they’re of course crucial to the operation of the weapon. We don’t usually consider the warhead and the rocket propellant to be exactly the same thing, but they both have to work if the weapon is going to work. I suspect there are many situations where the line between the “physics package” and the rest of the weapon is a little blurry. But, in general, the distinction seems to be useful for the weapons designers, because it lets them compartmentalize out concerns or responsibilities with regards to use and upkeep.
The shape of nuclear weapons was from the beginning one of the most secret aspects about them. The casing shapes of the Little Boy and Fat Man bombs were not declassified until 1960. This was only partially because of concerns about actual weapons secrets — by the 1950s, the fact that Little Boy was a gun-type weapon and Fat Man was an implosion weapon, and their rough sizes and weights, were well-known. They appear to have been kept secret for so long in part because the US didn’t want to draw too much attention to the bombing of the cities, in part because we didn’t want to annoy or alienate the Japanese.