Actually it's not that either.

Success in a business context means a positive rate of return on the resources invested. Or to refine one step further, a return that is positive and superior to the next best alternative for the deployment of said resources at a given level of risk.

So Profit.

ROI /= Profit.

See Amazon (or as noted below, Instagram).

However I also think that is a problem for many people who want to startup. They don't usually think about how they'll show a profit and manage to run their business within that profit. Investor money gets them started and an exit by selling an unprofitable yet growing business to a larger company is the goal.

Profitability and return on investment are related concepts but are not the same thing.

Instagram, among many others, most certainly generated ample return on its initial invested resources without ever generating profits.

Success can also be short term growth and being bought by a larger company, in this industry.

Success is the most loosely defined, illogical concept in the startup world. When your friends are raising big rounds, you think they are successful, even though most of them won't survive beyond the runway that round gives them (esp. at that stage).

Yet the media and the community celebrates founders for all sorts of things and call it "success" when it's not. So yes, it's incredibly vague, and the existence of an accounting formula means nothing in the founder psyche.