Analog is like an analog watch vs digital watch, analog being a cigarette and digital being an e-cig
Atomizer is a heating element used with a plastic and stuffing cart as part of a 3-piece ecig setup. The carts are a bit cranky, may give an uneven experience, can dump their juice and often need frequent topping off with juice. A cart can last a long long time - can be cleaned, restuffed with a particular blue foam or other material, etc. You can use any thickness (any PG/VG) of juice as long as it flows at least as fast as you vape. PG is thin and lets through the most flavor, nicotine TH and nicotine irritation. VG is thick and dulls everything PG lets through but adds thicker visible vapor.
A cartomizer is a combined one-piece cart with built in atomizer coil - they hold more eliquid, generally need liquid less often, provide a more even vaping experience, won't dump all of their juice. But they are disposable. A couple of higher end kinds are supposedly designed to be cleaned and some people try to clean normal stuffing cartos with mixed results. The stuffing cannot be replaced. I just use for for a week or more then start a new one. They cost $2-3 each. Most cartos work best with thin juices. I use juices with 20% VG or less. The most popular 3-piece ecig threadings also have cartomizers available but almost all are blank cartomizers. The most popular 2-piece ecig threading (KR808D-1) has plenty of prefilled and blank cartomizers. Cartomizers are probably the most popular way to vape.
You buy stuff in advance to stay stocked. You can never know when vendors will run short on carts or cartos (and BTW you probably never need to own more than 1 pack of carts ut you should keep cartos stocked). And sometimes a vendor will run out of a juice flavoring or if the juices are made for them in China they may run out of your nicotine level in your favorite juices.
And re buying in advance - that includes SPARE PARTS. If you use atomizers a lot, you should have at least 3: 2 to swap while cleaning one, and 1 total spare. It is good to have a 3rd battery (and I super strongly recommend manual batteries). it is good to have spare charging cables (plus handy to have one at work and enough at home to charge 2-3 batteries at once). New vapors are the ones who run out of juice or cartos (or carts if they didn't buy juice), who have no spares and whoops kill two attys and are left with no others and no cartomizers, etc. Veteran vapers have lots of juices and various cartos they tried and multiple models of ecigs.