It seems that the internet allows for a third option: a small company that grows slowly and organically which eventually captures a significant market segment, still staying small. GitHub was like that for many years since founding. Linear apparently is another example.
But like palata said above, it is a startup if hasn’t found product-market fit.
As soon as it is profitable, it is a normal company. Small or big.
An established company has established products and keep building/improving them. A startup does not have that: they just have ideas and try them until one works, or they run out of money. VCs consider it's worth fueling that "trial-and-error" with investments because they believe it is a competent team in a promising field. Nothing more, nothing less, it's just a lottery after that point. Just one where VCs and founders like to believe they are enlightened.
Because the first idea you try is successful does not mean you know more than the (numerous) others, but rather that you were lucky at the first try.
Maybe it's my own personal bias but I feel that these stories of low,
slow growth; small teams, small wins but consistency are becoming
more norm. While I realize there is still plenty of froth, it's
inspiring and makes me hopeful for an industry shift in that direction.
They had 50 users after two years.
"And when we launched after a year in private beta, almost all of our 100 beta users converted to paid customers." — That's a neat stat and one I'd be extremely proud of.