2-piece ecig setup is battery + atomizer aka atty + cartridge aka cart (cart is plastic and stuffing)
3-piece ecig setup is battery + cartomizer aka carto (a combined one piece disposable cart w/ internal atomizer)
Cartomizers usually hold 2x or more the juice amount vs carts, keep each flavor separate, need juice added less often, provide a more consistent vaping experience. There is a bit of a learning curve for filling them and learning to keep them damp, and if you use appropriate juice a carto can work well for 4-7 days or more.
I use an atomizer to test juices and to vape ones that did not earn cartos. ANd my favorite thinner juices get cartos.
For slim ecigs, I recommend only manual batteries. Manuals are sealed better or totally on the threaded end so they are safer from being damaged or killed by juice leaks. manuals will not turn on accidentally from wind or vibration. And manuals make it easier to get a good hit.
Decent slim ecigs - the two most popular most supported models are Joye 510 (don't buy clones, the standard batteries are 180mah so small but short life and the mega xl ones are quite long with 280mah charge) - see Liberty-Flights.com and LiteCigUSA.net for Joye 510, see FreedomSmokeUSA.com and elsewhere for Joye 510 mega xl. And the other popular model is KR808D-1 (2 variations - see Vapor4Life.com and SmokelessImage Volt and I recommend the standard/78mm batteries which are 280-320mah charge).
Joye 510 comes as a 3-piece and there are plenty of blank cartomizers for it, the most popular being the Boge standard resistance. KR808D-1 comes as a 2-piece so there are plenty of refillable prefilled cartos for it plus a good variety of blank cartos, and a DSE901 standard resistance atomizer can he used on it to test juices and if you bought manual batteries like most here use and recommend then you can use a drip tip to test juices.
Note - there is a Joye 510-T with tanks - I would avoid that as a starter only because their charger can damage other 510 batteries. if you choose 510 start with normal or mega 510 manual and you can always put a 510-T tank atomizer and 51-T tanks on the normal 510 batteries if you want to try tanks.
Beyond that are non-slim fat battery models (see Ego and Riva 510 at Liberty-Flights.com after pressing their 10% off on front page) and mods that provide longer battery life and the ability to use the hotter low resistance (LR) atomizers and cartomizers.