A strong leg drive to start is used in both lifts.
A push press is after the leg drive, you finish with a pressing of the shoulders. Your feet don't leave the start position and your legs are straight.
A push jerk is after the leg drive, you have to catch the bar with the arms locked. There is no pressing of the shoulders. In order to meet the bar with locked arms, you will have to dip your legs a bit. If you have to dip deep to catch or ride the weight into a squat, it is a squat jerk.
A split jerk is after the leg drive, you split your legs to catch the bar in the overhead position with straight arms. No pressing out of the bar is allowed.
These aren't exercises you do for hypertrophy. They are for total body power. 10X3 wouldn't be bad to start, since you will be using lighter weights to learn the exercises. As you get better and use higher weights it would be very difficult to do that much work. Maybe 10x1 or 5x2 would be better. There is a technique to learn in these movements so be patient.
For general ahtletic training the power clean and push press is a wonderful movement that'll improve your power without having to learn the intricacies of the clean and jerk. The jerk is a much more technical movement.
If you do heavy split jerks, do about 5-8 sets of 2-3 reps at about 3 min in rest if your more fast twitch oriented. A little less rest if your not. Jerk's are more an athletic movement, which are golden if your focus is for whole body speed and power.