Say like foot locker or Zappos for a "shoe store" (both big business) and say McDonald's or Olive Garden for a restaurant.
By the same measure, we're building 37signals to grow as well. Grow revenues, grow customers, grow influence. We're just not that hooked on growing head count or office space (which are often the most visible indicators of growth for a private company and thus often mistaken as the only indicators).
To me a startup simply means a new business that's getting off the ground. That business may well end up big one day and it may not, which is okay too.
I generally don't think that you can become a star by trying to be a star. I think you just try to be the best at what you do and if you are, hopefully the star part will take care of itself.