Fitzgerald likes to play with the distinctions between "old" and "new" money. The idea of those who inherit wealth as part of their name and the behaviors associated with it versus those who recently acquired it and wish to be considered in the same league as those who are established visions of wealth is of significant importance to Fitzgerald. It also helps to underscore both men in Daisy's life.
Gatsby is a construct of "new" money or the "new" rich. One reason why Gatsby would represent the "new" rich is because of his own self definition. Nick describes Gatsby as who "sprang from his Platonic conception of himself.” Gatsby is an example of the "new" rich because of his own rejection of his past. Rejecting the narrative of a Midwest farmer background and Jay Gatz, Gatsby was able recreate his own being. In doing so, he embodies a form of the "new" rich. The fact that Gatsby's means of making money is not something inherited from legacy or from family name is another reason why Gatsby is considered "new rich." Gatsby lacks the family title and distinction of someone like Tom. When Tom derides him with the idea that Daisy could never be with someone like him, Gatsby fails to realize that despite his money, he is still an outsider. Gatsby is an outsider, a form of "the other," because he will never be "old money." He will always be someone who wishes to be something he cannot be. Fitzgerald was mindful of the distinctions within wealth, reflecting the idea that faith in wealth is analogous to “a promise that the rock of the world was founded securely on a fairy's wing.” Gatsby embodies this with his "new money" status.
Tom Buchanan is an example of "old money." Tom's money is established and "old." It is a significant part of his characterization Nick illuminates within the novel's exposition:
His family were enormously wealthy — even in college his freedom with money was a matter for reproach — but now he’d left Chicago and come East in a fashion that rather took your breath away: for instance, he’d brought down a string of polo ponies from Lake Forest. It was hard to realize that a man in my own generation was wealthy enough to do that.
Tom represents "old money" in how his family was "enormously wealthy" and in the manner in which Tom carried himself. Tom's wealth is established and familial, representative of class and social approval. It it the type of wealth that carries privilege with it as well as external distinction. This is a condition of "old money" that Tom possesses that Gatsby will never achieve. It is an embedded difference between both men, and something that Daisy herself shows deference towards in her choosing Tom over Gatsby.
Old and new money refers to how people acquired their wealth. People of old money inherited their wealth. They now remain wealthy by growing their money in the stock market. Recall that the stock market was at record highs in the 1920s before the crash in '29. Tom and Daisy are examples of old money. New money refers to people who worked for their money. Gatsby is an example of this. They had no starting capital and had to work from the ground up.
"New" money and "old" money are the same thing on the surface; however, there is quite a difference on how it is acquired. Old money is what we think of as people who's families have had money for a long time. Old money isn't money that has been earned in the past decade or even century, but passed down from generation to generation. It doesn't necessarily have to be centuries old, but the idea is that anyone living hasn't had to work for the money that they currently have. In The Great Gatsby, Tom Buchanan is an example of someone with old money because he comes from a family with a lot of money and high social standards.
New money is just the opposite. The person who has the money has acquired the money on their own, and they didn't have much of it in the beginning. New money is often looked at as fleeting because it was gained so quickly it is often lost just as quickly. It is also believed that money that is gained quickly isn't always earned fairly. Jay Gatsby is an example of someone with new money.