I seriously hate those words, not their meaning of-course, but how wrong they are used. Let me explain:
Responding well to something means responding quickly and correctly. In computers and UI in general, this refers to how fast e.g. a press of a button results in its designated action. If you need to fetch stuff from servers and these are responding slowly, your UI have bad responsiveness. If the server is dead, your webbapp is not responsive at all.
Adapting to something is adjusting to new conditions, like how evolution adapted fish when they climbed up on land. It is something more than the realisation that windows have variable sizes, and your users might have them small to have room for other apps, sometimes bigger, and sometimes fullscreen (and they might have different sized screens too).
This is probably nit-picking, obviously you can say "responding to change of window-size" or "this UI is adapting to a different window size", but honestly, how does that sound? What about "architecting my gin n' tonic" or "constructing a sandwich"? Clearly "adaptive" is better than "responsive" since it's not already taken, but still, way too ugly.
I prefer the word "dynamic". A dynamic layout has variable sizes, it can shrink to a small layout, and grow to a big. It can have dynamic width with a fixed height or it can be dynamic in both axes.
The irony here is that dynamic also means something else. If you were around in the 90's you could read books about "dynamic HTML". Since you are reading this today it might be hard to understand what this is and what makes this different from any other website, since basically they are all "dynamic" in the 90's terminology.
This leads up to the final K.O blow of the ugly words "responsive" and "adaptive". You cannot make a website today that doesn't have a variable width, just as you cannot make a "non-dynamic HTML" website (how would that look?). There is no going back, the bar has been raised. So these words are, or will soon become, meaningless. Just like nobody is asking if webpages use CSS - it's already assumed. Instead of starting to use the word "dynamic" to describe variable sized UI, let's just call it "regular website".
I still maintain couple of irregular websites, but soon I hope to make them all regular.
Ha! No, this sounds too weird... But I'm out of suggestions. Do you have a better phrase? Or perhaps we should just wait and let time clean up the terminology for us.