Gatsby and Nick live in West Egg. Tom and Daisy live in East Egg. the greatest distinction I see is that the West contains "new money" or money that is yet to be earned. In East Egg, money is so old and inherited that the people who have it live off can live purely off the interest. Tom doesn't have to work. In the East, we have the high class to the extreme. But so many folks, even from the East, are happy to go to Gatsby's parties and take advantage of the free fun.
The attached link gives an additional perspective of East and West and their meanings that reach beyond the Eggs and into the difference between East and West as our nation experiences it. Read under setting.