Yes. This is my favorite way to vacation, and I'm glad someone has found a better name for it. I do not enjoy simply sitting around idle and occasionally going on a trip, I end my time off feeling drained and need a vacation from my vacation.
One year, I had an itch to try my hand at Godot and game programming, and I saved it for my next vacation. I'd never felt more relaxed after a vacation, it's the same as what the author describes: I like being intellectually stimulated, I just needed a break from work, not from trying new things.
This article has helped me figure out some of what made that work, and has given me some ideas of how to try to capture that again.
I find staycations to be the same thing as a vacation but at home. Especially if you liv in more touristy places (NYC for instance), there's plenty of vacationy things you can take while not leaving more than 10 miles from your house. I like going to the beach or to my parents or what not (even going on trips), but I still need something to keep my mind busy. I hope that sums up the difference well.
This article has helped me figure out some of what made that work, and has given me some ideas of how to try to capture that again.