They have different names because they represent different technologies. and have different advantages and disadvantages.
Atomizer: Generally an atomizer has a heating coil at the bottom. Sometime the coil is covered by a metal mesh or wick. Material can be pressed or dripped onto coil. Generally dry herbs vaporizers will use this technology.
PROS: Great for dripping eLiquids. Simple design is easy to us. Often Low cost.
CONS: Need to refill a lot. Hard to tell how much material is left.
Cartomizer: Catomizers normally have a cylinder going down the middle with heating coil(s) in it. Normally this technology is used for eLiquids.
PROS: Hold more material. Fairly easy to rebuild and fix.
CONS: Often retains previous flavor
Clearomizer: Clearomizers are generally plastic or pyrex and have a clear (sometimes translucent colors) tank. Some have top coils, some have bottom coils. For eLiquids they will often have long or short wicks protruding from the coil.
PROS: Can see how much material you have left easily. Come in large capacities. Often rebuildable.
CONS: Usually more expensive. Some leak (not ours).
What matters most tends not to be the specific technology but instead the quality of the implementation of that technology. All types have great and horrible models. Vape Pens Sales strives to carry the highest level of quality products.