If it’s true that a pro boxer punches harder than an MMA fighter, what’s the major difference in their (punch) training?
It really depends on how you define the phrase “punch harder”.
Secondly, boxers are deadly from more angles since that’s all they do. MMA fighters will tend to avoid punching or evading punches from certain angles because they don’t want to get grabbed or kicked. They also don’t have time to learn all the possible angles (as well as their nuances) because they also have to focus on all the other skill sets in MMA.
For the basic 2–3 punching angles in fighting, boxers are 10–25% more powerful than MMA fighters. But for all the other 15–20 punching angles in fighting, boxers are infinitely more powerful because MMA fighters don’t even train at those angles.
Copied from my original answer on Quora.
A great example of this is the Conor McGregor vs Floyd Mayweather fight.
Conor McGregor is arguably one of MMA’s top pound-4-pound superstars, carrying his punching power up in weight and knocking nearly everybody down or out. But when a prime Conor McGregor faced a 40-year-old Mayweather with hand problems (and didn’t punch hard anymore), AND OUTWEIGHED HIM BY 15 POUNDS (or more), what happened?
Conor couldn’t even earn (the much smaller) Mayweather’s respect. Mayweather walked him down behind a simple guard taking some of his best shots for 8-9 rounds and then knocked him out in the 10th without breaking a sweat. So while I do think MMA fighters can box to some degree (they all have boxing trainers in their gym), they just aren’t competitive against boxers who spend many more hours just punching.