I would think a "duvet day" would be just hiding under the covers all day. And that might be considered "me time" too.
In my opinion, "me time" is time spent trying to figure our what I need and want, and trying to get and do those things for a while. To some extent, what one does on "me time" is determined by economic situations. So, for example, "me time" might mean spending an afternoon at a spa getting a massage.
I could use some "me time" sitting on a beach on Maui right about now, but I'm just a tad short of miles on my Gold Credit Plan. I'll have to settle for some "me time" on the couch with the cat.