Patterns of generation
The most common type of cave is one that seems to be a carved pathway. They can range between only a few blocks wide, to being relatively massive in size. When generated, the caves will replace all blocks in its path with air, except for a select few, such as sandstone.
In the overworld, caves have a chance to generate directly from dungeons.
Cliff caves and overhangs
When a cliff is generated, there's a chance that the generator will spawn a cave at its base. The caves generated are usually small.
Caverns in Mine Blocks are small reservoirs of liquid (such as water, lava, and acid), found deeper underground.
Caves generated in the nether are much larger in width, length, and frequency, yet otherwise identical to the ones generated in the overworld. They account for much of the generation time for the nether.