Thermal printers literally use heat to print, not ink at all. They have a heated printhead that darkens special thermal paper when it passes under it. So yeah, no cartridges needed whatsoever - that's the whole appeal. The paper itself is coated with a chemical that reacts to heat and turns dark. Pretty clever system once you understand it.
For shipping labels specifically, thermal is genuinely a game-changer compared to inkjet. You'll spend way less on supplies since you're just buying thermal paper rolls instead of ink cartridges, which get expensive fast when you're printing a bunch of labels. The printers are also pretty compact and reliable. That said, thermal paper is a bit pricier per page than regular paper, but you make it up on not buying ink. Plus thermal prints are actually pretty durable for labels - the image won't smudge easily.
The main catch is that thermal is basically black-and-white only. If you need color labels someday, you'd need a different printer. But for basic shipping labels, address labels, and that kind of thing, it's hard to beat. The setup is dead simple too - just roll in the paper and go. Coming from an inkjet, you'll probably notice how much faster and less hassle it is.