The Elohists and the Jahwists are two of the four different sources for the Torah (and thus the Old Testament) - the other two are the Deuteronomists and the Priestly source. (And I made a mistake in my previous post: The first two chapters of Genesis are from the Jahwists and the Priestly source, not the Jahwists and the Elohists, but the point still stands.)
The names come from what they believed to be the name of God. The Elohists are named for Elohim (supposedly what God was called before his name was revealed to Moses - it is actually the plural of Eloah, which in turn is the Hebrew cognate of the Arabic Allah, and is the reason so many of the angels (and Israel itself) have names ending in "-el").
The Jahwists, on the other hand, are named for Yahweh (and are sometimes called Yahwists instead).
There are other differences beyond the names, of course. The Jahwists saw God as more human-like than the Elohists, for example.