I feel that if my objective is to get rest, but be lightly aware of my surroundings, then I'm catnapping. Catnapping would be how I used to rest when I was dreadfully tired, and Critter was awake, but could be occupied by watching his Butter Battle video. I don't remember what occupied Tigger enough for me to catnap. Catnapping is often all I do when I'm extremely aware of the time, and am responsible for something directly after waking.
Napping, on the other hand, is where I let go and fall deeply asleep, and most probably need external means of waking, since I usually only nap when I'm short on sleep, and don't often have the time available to sleep and then wake naturally.
This morning, I took a catnap, and then a real nap.
The catnap was most appropriately termed, since my reason for being lightly aware of my surroundings was dogs. When I got home from taking the boys to school, I let the dogs in from the back yard and played with them for a bit. Then I sat on the couch to read and give them couch time. They settled into a arrangement with Dizzy taking my chair, Ouchy sleeping by me, and Flood nesting in the blankets at the other end of the couch. I started out reading. But apparently getting six hours of sleep last night wasn't enough to catch me up. So I catnapped. Flood was the first to show signs of restlessness, and when I got up to take her outside, the scotties followed happily. They had gotten enough quality house time, and were ready to play outside again. I love my new fence.
Once they were safely outside, I took a real nap, until I was awakened by my cell-phone.
And now I've had enough rest, and plan to stoke up with some sustenance, and get to some serious housework.