So what is the different between a cartomizer and an atomizer? The simply explanation is that a cartomizer is a cartridge that contains a disposable atomizer while an atomizer is reusable and is attached to a cartridge which is usually refillable.
For instance, below is an atomizer. This is essentially the heating element that screws onto the electronic cigarette battery.
And here is a mouthpiece with a cartridge in it (pushed out using a toothpick) that slides over the atomizer (shown above). The little white cartridge shown can be filled and refilled with e-liquid. The mouthpiece slides on and off of the atomizer for easy refilling.
Now, compare that to a cartomizer, shown below. The cartomizer has an atomizer and a cartridge together. They do not come apart. Although some do manage to refill cartomizers (by popping off the end), for the most part they are one time use.
Refilling your own cartridges is cheaper. Using cartomizers is more convenient. The choice is up to you!