Hey Bigjim. Yes this stuff can get kinda confusing. Let me try to clear things up a bit.
Originally, ecigs were designed to have a cartridge that holds liquid, which you are referring to as a mouth piece. It would hold a lot more than 2-3 drops. I'm not exactly sure how much liquid it holds as I have not used a cartridge in a long time. It's supposed to last you about a packs worth of analogs I think. Someone correct me if I'm wrong. Like I said I haven't used cartridges in awhile lol.
Most people find that cartridges just don't work all that great, so we've come up with direct dripping. This is a technique where you drip 2-3 drops directly onto the atomizer. Not the mouth piece. You get about 5 good puffs then you repeat. Hence our slogan...drip, vape, repeat.
Now there's these new things called cartomizers, which I have yet to try myself. It's a 1 piece atomizer/cartridge combo that's aimed at keeping things low maintenance. They are meant to be disposable, so once it's finished you just throw it out. I've heard you can refill it though, about 3 times before it completely goes bad. And yes, this just screws right onto the battery.
Hope this helped a little and not confused you even more.