A bit of both. Nukes in this universe traded explosive yield for radioactivity, so thats why all of the major cities you see in the game are still standing, but also still have pockets of radiation kicking around whereas with real life bombs the majority of the fallout would have decayed in a month or two. To put it into perspective there's some lore thing I read where a week after the bombs there was a black rain that killed off the majority of life that managed to survive the blast, whereas in real life black death rain is something that as awful as the war would be, is obviously not going to happen.
There's also the whole suspension of disbelief thing going on, there no actual reason why the buildings would be standing in 2161, some 80 years after the war, which was the first games date compared to Fallout 4s 210 years. Just what needs to happen to make the game actually fun.
Its also worth noting that because we haven't had a real life nuclear war the actual real world effects of what would be the biggest catastrophe to afflict us aren't really 100% pegged down. Some people say that the entire of North America and Europe would burn down into nothing, with the giant firestorms resulting from the blast. Some people think that although the world economy would collapse, you would have South America escape unharmed and truck along with only dire economic conditions instead of a actual apocalypse and complete breakdown of society that we see in much more fiction than just Fallout.