There's some very solid information here but there's a big part that's missing. The fact that there are three separate kinds of muscles and developing each is a completely different process. I'll use takedowns as an example since that's an application of explosiveness that everyone sees in a similar way, where as applied hand movement is too variable.
The first is slow twitch muscle fibers (type 1). There muscle fibers use are highly oxygenated and apply most effectively in MMA for endurance. Circuitry is the best way to develop these. However in the case of these, they apply little to explosively strengthening the bench press, or developing quick hand movement. These are developed through lifting for many reps at a moderate pace. I only noted them so there is a reference point for type 2's. Think of the muscles used here in the Jake Shields style takedown, enduring and pressured, but with little explosiveness.
Fast twitch muscle fibers (type 2a) firstly. Type 2a muscles are strength muscles. These muscles, while possessing a protracted explosiveness, do not work at the extreme pace needed for true explosive lifting. These muscle fibers to not reach their full contraction as quickly as type 2b fibers and thus, are not as explosive. These muscle fibers are developed through heavy lifting at the approximation of an aggressive pace. Here, think of the Phil Davis or Josh Koscheck style power double leg that's not the fastest, but is strong and overpowering.
Finally, type 2b fibers. These fibers are where true explosiveness comes from. These fibers achieve full contraction in the shortest period of time and, while not producing as much kinetic energy as type 2a, produce the energy far faster. These fibers are developed through lifting moderate weight as fast as physically possible to the point where the weight defies gravity. In the case of the bench press, the weight would have to feel weightless in the palm to be true explosive benching. Here, think of the GSP style single or double leg that is a single bursting movement to which it is very difficult to react.
As was mentioned by North, some lifters do a split where they lift heavy, and another separate dynamic day. These lifters are working both forms of their type 2 muscle fibers. Which makes sense, since powerlifters would need to activate both the rapid contraction, and strong contraction fibers in their muscles to lift the extreme weights they use in competition.
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I went out the way that I fight. I went out on my shield. That’s it. Done. --Chuck Liddell
My goal is to end my opponent --Carlos Condit