Crimpers and Pinchers
These tiny holds require a climber to crimp or pinch with his fingers to make contact and move up the wall. Crimpers can provide a tiny ledge for a toe when moving up but are generally harder to grab hold of with the hands. Pinches, though still difficult, allow for more of a grip between thumb and for fingers. Both of these types will build strong finger muscles.
Like the name implies, these are shaped with an indentation like a pocket that allows for a fairly secure grip. The fingers hook on to the ledge of the pocket, and some may provide a secure enough hold to hang from.
Jugs and Jibs
Jugs, also known as finger buckets, are some of the easiest holds manufactured and can be found on most routes rated up to 5.9. They sometimes are called jibs and come in a variety of shapes and sizes, but what they all have in common is some sort of large feature that hangs or protrudes out and requires minimal strength to hold on to.
These are also pretty easy as far as gripping goes. They are made to protrude off the wall a fair amount, and one can generally find a good ledge to pull up on with the fingers or stand up on with their feet, though they are not as easy as a jug. If you were to grab an ergo with super-sweaty hands, you might not be able to stick it, whereas you could probably hang on to a finger bucket no matter what.
These climbing holds are somewhat hard to describe, as they come in any blob-like shape that may require crimping, pinching or any other move.
There are many more types of climbing holds. Some are classified as "naturals" because they are made to imitate a certain texture of rock as well as shapes that are commonly found on a certain type of rock, such as hybrid sandstone, limestone or granite. There are also many extra-large holds that may be shaped like a skull, egg, dinosaur, bunch or grapes or large flake of rock. There are also minis that come in the main shapes but are smaller.