[jevans]

But the idea is that the site presents itself in a way that is optimal based on the medium being used by the user, right?

Why would "degrade" be the better way to refer to that idea?

[nchlswu]

I believe the initial logic was due to legacy browsers such as IE6. These are browsers that aren't what you designed for, so the webpage degrades. Since you take some steps to mitigate this and optimize it when it degrades, it makes it "graceful degradation"