Well, I feel the two work hand in hand, but fear can help a trader exit from the market with a little profit instead of sitting too long, while greed can actually cause a trader to overstay in the market until they begin to see losses again after they have failed to cancel the trader when they were really in a great profit zone.
Take, for example, you opened a position with $1k, and after like 10 minutes, you are already seeing a +50% profit, which is $500. Instead of you canceling the trade and just taking the 50% profit, you decide to stay in the trade for a little longer. I think that's greed because the market is dynamic and could turn against you. If you also cancel the trade and a few minutes later the market keeps going higher in your direction, it can be said that fear has actually made you exist in the market so quickly.
In my opinion, fear does more harm than greed. Greed can actually make a trader look foolish in the market in the sense that after seeing a profit of 50–100%, you decide to wait for more profit and on the process of waiting a little longer, you begin to see losses again.