Nothing!
Thin thigh high socks are usually more elastic. But the upper limit of elasticity is not determined by the thickness of the socks, but the band on the top of the socks will determine whether these socks have sufficient elasticity. Elastic bands can be stretched to more than 4 times their own length, and they are not easily deformed. But this has nothing to do with the thickness of the socks.
Thin thigh high socks look more breathable. But what actually determines the breathability of socks is the material and weave, not the thickness. Ordinary plastic bags are very thin, but they are not breathable. Some cotton children’s sleeping bags are thick, but they are very breathable. Water shoes look thin, but they are even waterproof. The knitted socks look thick, but they are full of small gaps and holes.
Thin cotton thigh high socks have no advantages, none at all. Then why do manufacturers still produce them? Low cost is the only reason. Kayhoma is completely different.