When someone "dozes off," they fall to sleep for a brief period of time. They may not have had the intention of falling asleep, but they did anyway...this often happens when someone is watching TV. "Taking a nap" is when someone goes and sleeps for an hour or two during the middle of the day. For example, after I am done with classes I am usually pretty tired, so I take a nap around 2pm so I feel refreshed when I wake up

Take a nap=> You intend to sleep for a short period of time. Voluntary, within your control. Doze off => You did not intend to sleep, but then you fell asleep. Not within your control. EXAMPLE: 1. I took a nap for 10 minutes before heading to work. 2. I dozed off while waiting for the bus.

Doze off: to go to sleep especially when you did not intend to. for example: I was so tired I dozed off in the middle of meeting. You also can use "nod off". It's a synonym for "doze off". Take a nap or ( have a nap ):a short sleep, especially during the day. Foe example: I am really tired, I should take a nap. Hope this help :)

take a nap = sleep　寝ている doze off = fall asleep 寝付く