You can drip on either, but dripping on a carto is usually called "topping off" and is a fairly typical carto use technique.
Dripping is done on an atomizer and usually an atomizer with drip tip. The drip tip replaces the cartridge. You can drip on any atomizer, but some are more suitable than others. Some drippers like bridgeless atomizers, but I tend to like dripping on atomizers that have a bridge. Dripping on an atomizer that has a needle cap, like the C-types, is difficult and not worth the effort in my opinion.
My favorite atomizers for dripping are the I06 from Ikenvape and the HH.357 from Avid Vaper. The I06 requires a specific drip tip while the HH.357 can use any 510 or 901 drip tip, but the I06 is less expensive. If you decide to get one of these be sure to read how to prime and break in the one you get.
Once you have a dripping atty broken in you are now ready to attend a
vape meet and sample the selection of different juices there, or just drip what you have and become known as a dripper. Hello, my name is Hoosier and I'm a dripper...