A cooler and an ice chest are the same thing.

None. They’re just different names for the same insulated box that keeps stuff cold.

“Cooler” is more common in the US South and West, and “ice chest” is more common in the Midwest and parts of the North. Some people use “ice chest” to mean a smaller, more portable one, but that’s not a real rule — it’s just how they talk.

If you see them sold in a store, the difference is marketing, not function. Pick the one that holds what you need and doesn’t leak melted ice all over your car.