There are slight variations in how high or low to hit, the vector... but those are pretty much just things to argue with over a beer. The real difference, the reason that there are so many variations is that it is pretty hard to get your own arms out of the way.
We never explain it that way. Each of the grips has advantages and disadvantages, a place and a time. Morote seoi nage works very well for shorter, stronger judoka; ippon seoi nage is nice when you have the room to fling an arm and is much easier than morote if you are slightly taller than your opponent. That's what we tell our selves.
What is really going on is that a hip throw requires a really tight connection between the two bodies. Especially in a full-entry hip throw, your arms aren't really designed to hug something behind you. The elbows push things away, the shoulders don't go there. The key to the variations is that they are just different ways of overcoming the fact that we are physically in our own way to accomplish that goal in that position.
Making a 'proper fist' is a really big deal for beginning karate students. It is taught in great detail, great precision and the student practices again and again until his or her fists ideally become little bone clubs on the end of an arm.
It's cool, but it's completely unnecessary. I know. Shock, horror. The first time someone explained this (it was Mac, by the way) I reacted as if someone had pissed on one of my religious icons. There was no way I had worked that hard to do a simple thing right that was completely unnecessary...
But it was. The idea with a punch is to focus the power through the ends of the metacarpals. Curling your fingers tightly beginning with the distal joint and working in then locking them down with your thumb accomplishes that. So does simply letting your fingers relax and hang down. You can hit with the exact dynamics of a karate seiken with completely loose hands. Both are just techniques for getting the fragile fingers out of the way.
In individuals this happens mentally as well as physically. People drop into sport mode when survival is the order of the day. They, sometimes, grip the weapon arm when they don't have the leverage to hold it even when the grip keeps them from getting the solid blow to the brainstem that they need to finish things.
And mentally- whether we call it the inner critic as writers do or a fear of success; whether it is self-satisfaction or laziness or complaisance-- we spend a lot of time getting in our own way. If you are like most people, the biggest obstacle in your road to success is you. What are you going to do about it? How do you plan to get out of your own way?