Atomizers:
These typically have a single coil wrapped around a silica wick. They usually have a wire mesh bridge over that, and possibly some vertical wicking to hold and control the flow of liquid into the atomizer.
Unless they are bridge-less or otherwise customized, most atomizers can be used with a second piece called a cartridge. The cartridge is typically a hollow plug full of polyfill. Saturate the polyfill with e-liquid and insert it into the atomizer.
Many people prefer leaving out the cartridge, instead using a 'drip tip'. They regularly drip liquid directly onto the wire mesh bridge and keep it wet at regular intervals. Some even pull the bridge out (or order debridged atties) and drip right onto the coils. Note, very few debridged atomizers will still work with a cartridge (Pump Carts are one exception).
Both atomizers and cartomizers can come with a wide variety of threading options.
510 and 901 are probably the two most common standards.
With the Provari, or Darwin, you get a 510 standard, and can use 'adapters' to attach anything else you might want.
With the Buzz, and a few other custom mods out there, you can either use regular adapters, or order different 'end caps' for the threading of your choice.
Regular 510 and 901 atomizers are popular for dripping. Some people continue to modify the carts for them and use those as well.
The 306 has become popular. It has 510 threads, but the bridge is fully exposed instead of there being a barrel or cartridge area around it. These are best used for dripping with a special drip tip designed for the 306.
Some like a 'bigger' atomizer platform.
Mega 510 is one example...larger stuff! The 801 as another example, has a little bigger atomizer with an extra wrap or two in the coil. The barrel is quite long, and designed to handle a much bigger cartridge than the 510 or 901 style. Carts with either of these large atomizer types do work MUCH BETTER than the standard 510/901 counterparts.
You can also get 'hybrid' dripping atomizers built around mega or 801 atomizers on 510 threading. For that matter, there are all sorts of 'custom hybrids' out there if you look for them. Ikenvape is a good example vendor that carries several 'hybrid' atties and cartos to choose from. By hybrid, they mean, mixing and matching various atty types to make a new mutant atomizer type
'Tank Atomizers', like the eGo T or the 510 T.
These have a wick plate over the atomizer coils and a single wick that carries the liquid down. They require separate tank-cartridges to hold the liquid.
Custom Kits, are also out there which allow you to wind your coils and install them. There are also things like the Genisis, USF, Fog, and so forth. Some of these have guts that you can replace screwing in a standard off the shelf atomizer, while others are geared so you can replace the actual coil itself with your own nichrome wire. Many of these rebuildable kits are pretty expensive and hard to get unless you build your own. You're on your own researching these...I don't know much about them.
Which is best?
Again, it's subjective...and depends on what YOU LIKE.
Give them all a try at some point....as your liquid collection grows, you'll probably learn that each type has a list of pros and cons unique to each liquid and vaping situation you encounter.