In the standard Techcrunch definition of "new", and "extreme", "new" is "new" and hasn't been done successfully before (or at least in the reach of the startup in question).
And "extreme uncertanty" usually means: you have a burn rate which forces you to rapidly achieve product-market fit, pivot, get more money, or give up. The above definition of "new" adds up to the "extreme uncertanty", as you are not sure what you are currently doing is something people want, and even if you pivot into something else, you will not be sure about it as well.
Therefore, a new old' fashioned bakery is a new business, but it is not doing something "new", neither has "extreme uncertainty" attached to it.
The "extreme" part usually conceives that you don't know if what you are doing is something people want. We know old fashioned bakeries is something people want. This can be seen on how much Eric Ries talk about "pivots". A bakery pivoting will not be an old' fashioned bakery.
Again, the definition is loose. Eric Ries' mentor Steven Blank has a more precise definition[1] which removes these cases:
a startup is an organization formed to search for a repeatable and scalable business model.
I don't think these definitions are made to replace one another, they are made to give different views of the same object. The same way an elephant is not a wall, snake, spear, tree, fan or rope[2].
Edit: Swombat recently argued[3] that the difference between a startup a and a lifestyle business is that a "lifestyle business" lacks vision.
[1] http://steveblank.com/2010/01/25/whats-a-startup-first-princ...
[2] http://en.wikipedia.org/wiki/Blind_men_and_an_elephant#John_...