The groin is where the elastic sits in traditional fitted underwear (panties for women, tighty whities or briefs for men), on the inside of the top of the thigh. If you look at a simple plastic doll that has legs that can turn and change their angle from the body, the groin is the place where the two parts come together (body and leg), near where the genitals would be if a doll had genitals.
To understand crotch, there are two things to think about. One is the crotch of a tree. That's a place where the trunk forks, and you end up with something Y-shaped. It's the part of the tree that's most vulnerable to damage from an ice storm, because the main trunk could split in two there.
The second thing to think about is rappers who grab their crotch on stage. I once heard a rapper explain in an interview with Terri Gross on Fresh Air that this gesture comes from fear. I'm sure there are other explanations related to bravado.
At any rate, groin is a precise location on the body, but crotch is more vague, it's that general area that would be covered up with a fig leaf in certain paintings.
When you go to the doctor and want to show him or her a questionable mole or bump or rash or whatever, you would not say that it is in your crotch area. Well, you could, but then the doctor would think you are a little crude. In this context, it would be much better to use a more precise word to describe exactly where the concern is located.
Inside/Outside
, like the difference between belly (the protrusion and surface area around the stomach) and stomach (the interior area of the belly).