It’s “shaken, not stirred” as opposed to “shaken, but not stirred.”
So, to order a martini “shaken, but not stirred” would suggest that (1) if a martini were shaken one might expect it also to be stirred, and (2) in this case a request was being made for said stirring not to be done. That would be ridiculous. I won’t go through all the chemistry and physics of shaking as opposed to stirring cocktails, and the details of gin-bruising and ice-chipping and breaking down of hydrogen peroxide that you can read in the insanely detailed Wikipedia article on the phrase shaken, not stirred, but obviously stirring is a much less vigorous act of mixing than shaking.
For various reasons, stirring vodka and vermouth together with ice, rather than shaking the same ingredients together in a shaker, produces a different result both visually and (to a connoisseur) in terms of taste. But if a martini has been shaken, stirring it afterward is pointless because it would cause no detectable change. And if a previously stirred martini is subsequently poured into a shaker and shaken, no one can tell that it had once been stirred. So neither way could the stirring possibly matter to Bond. He wants a shaken martini, that’s all.
The precision of language counts. [via daringfireball]