Elohim is an actual name of God used in Judaism; Yahweh and Jehovah are fictitious misreadings/mispronunciations by outsiders of the tetragrammaton (which Jews read as Adonai, not as any of those other forms). As for the difference between those two actual names in Judaism… that would depend on whether you accept the documentary hypothesis or not and whether you are asking the question from a religious standpoint or a historical/academic one.
Answering from the historical/academic standpoint, essentially the two names reflect the different beliefs of the northern Kingdom of Israel and the southern Kingdom of Judah; in the northern Kingdom of Israel, many separate deities called “El”s were worshipped and were associated with high places; in the southern Kingdom of Judah, the tetragrammaton was the name of one of the pagan war gods. Judaism was the result of the synthesis of these two religions. The shema, the Jewish declaration of faith, uses both names for God, effectively equating the southern deity with El Elyon (the El that is most high). For a while, the other Els and pagan deities remained a thing (they were just subordinate to the one Abrahamic deity), with these deities eventually being demoted to angels. The synthesis of these two religions also is the source of the apparent contradiction between the perception that God is in heaven (from the northern religion which associates deities with high places) and the belief that God is omnipresent (from the southern religion’s view of God).
From a religious standpoint, these are simply two of many different names for God with my previous paragraph quite contrary to the traditional religious narrative of the formation of the Jewish people.
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