essentially, most rockets use liquid fuel, while most boosters strapped on the side of the rocket use solid fuel (like on the space shuttle). boosters are a cheap way of adding more “boom” to your rocket, but they’re so inefficient you probably don’t want to carry them all the way to space.
there’s also hybrid fuel (solid fuel + liquid oxygen) which i didn’t mention because not a lot of rockets use it, and 4 panels isn’t a lot of real estate. it’s sort of a compromise between the two, and its what virgin galactic use for the spaceshiptwo.
of course “liquid fuel” can mean any one of a whole bunch of very different chemicals (hydrogen, methane, kerosene, etc) but that’s a comic for another day.