Startup is about starting a new business isn't it? If your first project was making money, but wasn't a business, with at least a rudimentar business plan, goals, and all the formality involved in doing real business... then maybe it was really just a web site that was making money as a side effect.

It looks like people enjoy romanticizing this darker side of starting up a new business. It's not your fault if you don't fail the first time you try :)