My understanding is that the Muschaweck minimal repair is primarily for “sports hernias” where weakness in the posterior wall causes pain, but there isn’t necessarily an actual hernia, or the hernia is small. I believe the genital nerve branch is typically cut in this procedure because it’s supposed to play a role in the pain in these particular cases.
The Kang method for direct hernias is for actual direct hernias, and not limited to small hernias. The genital nerve branch is not normally cut.
Both techniques are simplified Shouldice/Bassini of a more limited scope than the original. Not sure about all the differences.