Yup. Auto batteries are for cold cranking, namely, generating a lot of current for a short amount of time, e.g., 30 seconds, and then they need to be immediately recharged.

Deep cycle batteries are for extended usage between charges, and you can bring them down to 20% of capacity without damaging them. (Try that with a car battery.) You can get enormous capacities for deep cycle batteries for use on boats, RVs, solar powered homes, etc.

Sealed lead acid (SLA) batteries are very nice, as you can run them down, they hold their charge fairly well when not in use, you can trickle charge them so they're always ready to go, and they generally don't explode or leak.

There are lots of types of batteries and they all have unique performance characteristics, such as how long they hold a charge, number of recharge cycles, whether you can trickle charge them without damage (you can't do this to the Lion batteries), how fast you can safely charge them, whether they can be reconditioned, usable temperature ranges, etc., etc. Far more info to write about batteries than would fit here!

Companies like PowerPort will give you lots of information about how best to recharge their products.