Simple, both punches are same linear straight punch type but they have different range.
Jab/Lead Hand Straight Punch used for long range punch, it has longer reach like this.
Cross/Rear Hand Punch used for short range punch, it has shorter reach but very useful when you can’t launch a Jab Punch.
Same answer with the different between Round Kick and Hook Kick, both kicks are same horizontal swing kick type but their range are different.
Hook Kick/Lead Swing Kick used for long range.
Round Kick/Rear Swing Kick used for close range.

By the way, some martial art techniques are only effective to be executed with just 1 body part. For examples:
- Swing Chop only powerful to be launched with our rear hand, it less powerful if launched with lead hand.
- Back Chop only powerful to be launched with our lead hand, it can’t be launched well with rear hand.
- Uppercut only powerful to be launched with our rear hand, it less powerful if launched with lead hand.
- Backfist only powerful to be launched with our lead hand, it can’t be launched well with rear hand.
- Side Kick only powerful to be launched with our lead leg, it can’t be launched well with rear leg.
- Front Knee only powerful to be launched with our rear leg, it less powerful if launched with lead leg.
There is no 100% perfect martial art technique, there is no 100% fighting style, even legendary martial art masters and world champs are can’t mastering them all. All we have to do is keep training to sharpening our fighting skill and keep learning to expand our knowledge, choose which fighting styles that fit with ourselves then learn and master it well.
“Be Water, My Friend” quote by Bruce Lee is really work. If 1 technique failed then try other technique, if 1 technique didn’t work then try other technique, we must be dynamic like water and keep learning - sharpening our skill.