There is no such exact definition of success. people make their own according to them. The way I see it, everybody's definition of success can be mapped on a simple grid, with one axis being the amount of money that you have and the other being the amount of happiness in your life, like so:
There are two reasons why this definition is better. First, there's no point to being rich if you're not enjoying yourself. Second, you're more likely to get rich if you're happy doing whatever you're doing.
Being unhappy, of course, can definitely spur people to action. However, the action should be pointed at trying to become happier–not trying to become richer, in the rather naive belief that being rich, in and of itself, will make you happy.
Needless to say, if you're struggling to put food in your mouth and keep a roof over your head, none of this applies. When you're just trying to survive, you're not thinking about happiness.
Even so, I'd rather be poor and happy than rich and miserable.
Real Way to Get Rich
Of course, all things considered, I'd prefer to be rich and happy rather than poor and happy. However, I believe that it's easier to get rich if you start from a place of being happy–with what you're doing and why you're doing it.