Set means to “put in a certain place.” It is normally followed by a direct object, that is, it acts upon something else. It is transitive.
Sit means “to be seated.” It is always intransitive.
Incorrect: Set down on this chair.
Correct: Sit down on this chair.
Incorrect: Sit the money on the counter.
Correct: Set the money on the counter.
Set or sit plus a reflexive pronoun–“Set yourself down” or “Sit yourself down”–is nonstandard.
Set does not always take a direct object; for example, we speak of a hen or the sun setting.