Push press is often used by lifters towards the start of a program more as a strength exercise. The dip and drive is the same as a split or power jerk, the difference is that instead of drop under the bar to receive it, you follow through with the arms and finish in a fully extended position up on your toes. Don’t try to hold this position, come back down on to flat feet.
This lift of often slow to watch. In fact, it should be very fast and explosive. If it looks slow, it’s probably because the lifter is pushing with their arms before the legs have finished driving. The arms need to be relaxed or loose during the dip and drive to enable the legs to be most effective. The arms just guide the bar to overhead.
This is often used by CrossFitters when the aim is to get the bar overhead ‘anyhow’. If the weight is light enough, it is even quicker to perform than a power jerk, thus enabling more reps to be completed faster. Likewise with thrusters, a common exercise in CrossFit, as you stand out of the squat, think about relaxing the arms and exploding upwards, just allowing the arms to guide the bar to arms length.