Different types of grip strength are fairly separate and distinct. Grip strength can be narrowed down into four categories:

1 – Crushing Grip

Squeezing a hand gripper exemplifies this type of grip strength, but you need more than that for a strong, well-rounded grip.

2 – Pinch Grip

Plate Pinch

The best example of the pinch grip is holding two weight plates together, flat side out, and pinching them tightly so you can lift them off the floor. This demands superior thumb strength. Work your way up to pinching two 45-pound plates together.

3 – Supportive Grip

Farmer Walk

This form of grip strength is best demonstrated by holding onto a heavy barbell, dumbbell, or farmer's walk implement.

4 – Wrist Strength

Wrist Curl

Exercises like wrist curls and lever bar lifts, in which the wrist is maneuvered through different ranges of motion, characterize what can be termed wrist strength.

Train All Four Types

You may excel at closing a heavy gripper, but perform poorly on exercises like farmer's walks where high amounts of supportive grip are required. In addition, I've observed that the correlation between hanging onto a thick bar and a normal diameter bar is very low, despite them both being supportive grips. As the barbell diameter increases, the hand is forced open, which shifts emphasis to the thumb.

The take-home message in all grip training situations is that you'll need to train specifically for what you're trying to improve.

Related:  Massive Forearms, Strong Grip

Related:  Grip Training for the Deadlift