There's probably a few differences, but personally, I only ever care about three things - size, thickness, and being able to shake the sand out of the towel.
Size: Beach towels are a lot larger than bath towels so you can lounge on them while at the beach, lake or pool. You can use them to cover up better than a bath towel, too.
Thickness: Bath towels are thicker than beach towels so that they can absorb more water when you dry yourself from the bath, but thicker towels take longer to dry out. Beach towels are slightly thinner so the towel can dry out faster and you can continuously wrap up in them and lounge on top of them.
Less Sand: Sand can be shaken out of thinner towels easier than a thick heavy absorbent wet bath towel. Plush bath towels will hold in more sand.