The ability to generate force quickly is the undermining feature that makes someone explosive or powerful. Compared to strength, power has a time or velocity component - it’s all well and good to be strong (produce large forces), but to transfer effectively to most forms of athleticism this force needs to be available pronto. This is the essence of muscular power.
Rearfoot Elevated Split Squat - This might be producing a fair amount of force (pushing into the ground pretty hard), but it's occurring slowly. This is likely not training power, but rather hypertrophy or strength. Remeber, Power = Force x Velocity.
Same weight, but the movement is happening much quicker; both the eccentric & concentric portions. This should result in an increase in the Rate of Force Development of each rep. Time is the critical variable here - how quickly can the force be produced.
Turning the Rearfoot Elevated movement into a hop will result in a drastic increase in the velocity of the movement. Although there is no external load, the force and velocity increase will result in a higher rate of force development and hence will more likely train muscular power.
A slow Box Squat is a good exercise for increasing force production - training hypertrophy or strength, however, as the movement occurs at a slow velocity, this will not train muscular power.
Velocity and intention to move quickly has clearly increased here. Resulting in an exercise more geared towards training muscular power.
Vertical Hop - this exercise may have produced a lot of force, but the velocity is pretty slow; meaning it took a long time to produce the force.
Vertical Hop Quick - This demonstrates a quicker hop, with force produced at a much faster rate. This will maximise muscular power in comparison to the previous hop.
Powerlifting - This is incredibly strong (very high force), but not necessarily powerful (it's produced slowly).
Vertical Jump - This takes a tremendous amount of force, produced quickly - as powerful as it gets.
Power is the ultimate attribute of athleticism. Although to become powerful, you first have to be strong. But strong doesn't necessarily equal powerful. Time is key; moving quickly and with intent.