I like to make a distinction between a high crotch and a head-outside-single. One thing that you should probably understand is that this is less of a rule and more of a coaching preference. I started making the distinction when I was teaching kids in order to separate the ideas in my athletes' heads. If you have any insight into how you teach the difference between these two specific techniques, please get a hold of me. I'd love to hear it. 

What’s The Difference?

In the interest of simplicity, a head-outside-single is when you go towards your opponent and a high crotch is when you bring your opponent to you. 

Head Outside Single

I would venture to say — for better or for worse — that most people learn pretty much the same thing their first day on a wrestling mat. It's usually stance, motion, and then a penetration step. When we're talking about head outside singles we're talking about using that penetration step to attack one of your opponent's legs with your head on the outside. 

Descriptive Bullet Points:

• Penetration step
• Bring your hips to the leg that you're attacking 
• Find a way to either get back to your feet or finish from the mat

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Pros - Although most people only drill finishing this attack to a double, there is a multitude of different finishes that can be employed assuming you can knee pound your hips close to the leg that you're attacking. 

Cons - I’ve noticed that this attack is best suited for guys who are powerful and more compact. They have an easier time keeping their hips close to the leg. Longer body types have to be a bit more creative with the way that they finish from this position. 

High Crotch

If you’re looking for great technique on a high crotch, it’s probably best to go right to the source and start watching old John Smith matches, but if you don’t feel like spending the better part of your day in a YT rabbit hole then the video below of ASU assistant coach Chris Pendleton teaching this underhook to a Hi-C is probably the best that I’ve seen the technique explained. 

Descriptive Bullet Points:

• The tie-up that you use matters (elbow control and underhooks usually work best)
• Drop your level and pull them over you (DO NOT penetrate)
• Finishing up on your feet is difficult.

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Pros - One of the things that I enjoy about teaching Hi-C’s as opposed to head outside single is this technique can be used (well) by every body type as long as the person using it has taken the time to get a good feel for it. 

Cons - The problems with Hi-C’s are two-fold. First, it takes a long time to get a feel for this technique mostly because it’s not about what you do it’s about when you do it. Secondly, you had better get good at finishing on the mat, because it’s not very easy to finish to a double up on your feet. 

Just in case you feel like going down a JWS wormhole here’s a good place to start.