Questions about different atom smashing / splitting methods

[Curiouser]

1. We have read that when atom bombs were let off and nuclear power stations entered operation, there was a big rush of heat, which lends support to the idea of atoms actually having been "split" apart (to cause that energy).

2. We have also been told from time to time that atom "smashers", whether in the Kaku family garage, or miles of tunnels under Swiss Alps, are investigating numerous kinds of sub atomic particles that can be made to pop up.

Are the procedures in 1 and 2 above, closely related to each other, or actually rather different?  In particular, why doesn't "smashing" (2) need coolants?  And what does "spent fuel" (1) consist of if it isn't actual elements any more?  Did the two branches of technology actually diverge out of different scientific fields of research at an early date?  Is the apparent overlap or near-overlap in vocabulary genuinely confusing?

[HallsofIvy]

The only difference between an "atomic bomb" and "atom smashing" (Does the AEC know about the "Kaku family garage?) is that the latter is controlled.  I can't answer your question "Why doesn't "smashing" (2) require coolants" because it does!   Cooling is an important part of the "controlling" the reaction.

I don't know what "overlap in vocabulary" you are talking about.  Can you give a few examples?