These descriptions are very general, but will give you an idea of the differences between atomizer/cartridges and cartomizers.
Atomizers will work well if you plan on using cartridges or dripping. Cartridges are easy to refill and will last a long time and the filler is cheap to replace. There are plenty of fill mods and Zero Filler Mods (ZFM), but leak is still a problem. It takes a bit of trial and error to find a combination that works for you. My fiance really likes the 510 XL attys and carts. I used to really like the eGo Mega attys and carts (yes, they are two entirely different things.)
Cartomizers are an atomizer and cartridge all in one piece. There are two types; those which use filler and ceramics which do not have any filler. Some can be refilled by just popping off the mouth piece and dripping
juice on to the filler until it's wet. Some, like the the eGo Mega cartos and the ceramics need a syringe to refill them. Both types are intended to be disposable after "a few refills", but many people will clean them and reuse them until they finally just stop working or start tasting bad. The cartos with filler can have a really bad, cottony or burnt taste, especially if the filler becomes too dry and burns. Most ceramics don't have this problem because they don't have the filler. Juice is wicked into a ceramic cup, so there usually isn't a burnt taste. Both of these can leak when overfilled and refilling can sometimes be difficult because you can't see how much juice is still in them and you might need a syringe. There are some clear tank CE2 ceramic cartomizers that take the guesswork out of how much juice is still in there.
I've been using the CE2's lately with great success and it's by far my favorite way to vape on the go.