Quite different.

"I have little money" implies you have a very small amount of money, and usually less than you'd want to. For example, when your kid asks you to buy him a toy, and you reply "Sorry, I have little money", it implies you can't afford the toy.

"I have a little money" implies that while the sum in question might not be big (relatively speaking), it's good enough. When you tell your kid "Well, I have a little money", you're affirming that you can, in fact, afford the toy.