what the three sizes change
Small, medium and large are chosen once and cannot be changed later. A small world is 4200 tiles across and 1200 deep, a large one is exactly double in both directions, which makes it four times the area. Medium sits between at 6400 by 1800.
Distance is the obvious difference. Quantity is the one that matters more. World size sets the ceiling on how many of nearly every generated feature exist: chests, pots, Floating Islands, Pyramids, Jungle Shrines, Enchanted Sword shrines, evil chasms, altars, abandoned mine tracks, meteorite sites, and how many of the three Dungeon wall styles show up. Those are ceilings, not promises. A structure that finds no valid spot during generation is simply skipped.
the case for small
Most of the time cost in a run is walking, and a small world halves it. A hellevator is half the digging. A skybridge or a hell bridge for the Wall of Flesh is half the blocks. The Dungeon, the Jungle and both Oceans are short trips rather than expeditions, and a teleporter network costs a fraction of the Wire.
Small worlds also compress the layers. Floating Islands sit lower, so you find them earlier and reach them with a worse mobility setup. Wyverns spawn nearer the ground, which cuts both ways: farming Souls of Flight is trivial, and so is getting jumped while roofing a house. Ore is easier to find because there is less rock between veins, liquids are quicker to fetch, and the Corruption or Hallow spread is a shorter front to trench off.
the case for large
More of everything you break open. More chasms means more Shadow Orbs or Crimson Hearts, which means more rolls on their drop pool and more chances at a Meteorite landing. More altars means more Hardmode ore, since each one you break seeds another batch. A larger Jungle means more Life Fruit growing at once and a Temple carrying more traps and more Power Cells.
Space helps in fights too. The Underworld is longer, so the run from the Wall of Flesh has more track behind it. The Celestial Pillars land further apart and are less likely to sit on top of your town. Layer transitions are more gradual, and there is more depth that the game still counts as surface, which is where you hide tree and mushroom farms that refuse to grow underground.
what large costs you
Generating, saving and loading all take noticeably longer, and the world holds more in memory. On a weaker machine that is a tax you pay every session. Containment is harder as well, because two Hardmode stripes across a wider map is more trench to dig and more ground to clean afterward. Meteors work against you at scale too: the game stops dropping new sites once enough meteorite tiles exist in the world, and a large world tolerates more of them, so more of them land and more of them land on something you built.
picking one
Medium is the right default when you have no particular plan. Choose small when the world has a job: a farm world, a second evil biome to import materials from, a run you want to finish, or a first playthrough where seeing the whole map matters more than having one of everything. Choose large when this is the world you intend to live in and you already know you will build teleporters instead of walking.
Several small worlds often beat one large one. Nothing stops you carrying material between them, each new world rolls a fresh set of chest loot, and you can wreck one without regret.