I think that any useful definition that is useful for explaining evolution to laymen must contain the concept of natural selection. Here's my version:
Evolution is a gradual change in organisms over many generations caused by the combination of (1) random variation in genes among individuals and (2) the fact that those individuals that best survive and reproduce will transmit their genes to the next generation.${}^1$
That random variation arises (in part) from mutations is just a detail, in my mind. The fundamental mechanism, which is very hard to deny, is that even though variation in any individual's genes are completely random, the combination of this variation with survival of the fittest will produce a strong tendency to adapt to the environment. If someone has difficulty accepting / understanding this principle, it's easy to setup computer simulations that demonstrate the effect hands-on. In my experience this convinces pretty much everyone.
The "bait and switch" argument on the page you link to is fundamentally flawed because there is no difference between what they call "adaptation" and "evolution". Both are evolutionary processes, resulting from variation and natural selection. It's just that these creationists are willing to accept some consequences of evolution, but refuse to accept all of them. This is just a rhetorical device that lets them accuse scientists of "equivocation" (which sounds pretty sophisticated). Also, there are the usual falsehoods: "no intermediate forms", "mutations do not generate new information", and evolution is "just a hypothetical philosophy without observational scientific support".
But then again, creationist do not really care about the scientific arguments --- they only pretend to do so because they know science has credibility. They are driven by belief, and arguing with them is usually pointless.
${}^1$ I am aware that this is not the most general definition one could give, as it does not encompass genetic drift and other mechanisms described by modern evolutionary theory. But I think it's an appropriate one for explaining evolution, as in the discussion brought up by the OP.