Anyone that has bettas knows that fish sleep.
There is absolutely NO way you can misconstrue a sleeping betta as simply resting. They often turn pale and they're usually very very hard to wake up. Both of my bettas will go in their little "house" at night, lay on the bottom and drift off to sleep. At times you can tap on the glass for several minutes and they barely stir.
Heck, earlier today I thought one of the bettas at my LFS store was dead. I tapped on the tank several times in passing while I was there and he didn't move at all (No I don't usually tap tanks but if he was dead I was going to inform them). My husband stick his hand in and tapped the fish which FINALLY woke up and started moving around. I don't think you can assume a fish like that is simply taking a short rest, lol. When I rest I'm normally at least slightly aware of my surroundings.
I think it's pretty interesting observing different species of fish sleep. A lot of them do it in completely different ways. You can also observe some fish that are deep sleepers acting groggy like a human would when they wake up in the morning, at least that's how I perceive it.
When my Anostomus goes to sleep at night he goes into one of the decorations and loses most of his pattern. He won't come out until morning unless he's disturbed. In the morning, if he's not awake when the light is turned on, he slowly floats out of his decoration and his coloring and pattern will slowly come back. He's very slow moving and "groggy" looking at this time and seems to be having a look at his surroundings.
When my livingstoni sleep they huddle together and lay in the rocks. Unlike some other species which get pale, they actually get darker and gain a more vivid pattern. You can see them jostling each other periodically and some will temporarily awaken when bumped by one of the other fish. Sometimes this causes a bit of a spat if several end up waking each other up, kind of how I'd imagine several people trying to sleep in the same bed. It's kind of cute actually, lol. Upon waking in the morning they're very twitchy. Each wakes up and shakes a bit, and they each start reastablishing their positions and territories for a few minutes until everyone is situated.
Hmmm. I really should videotape some of this, it's a little more interesting to watch than read, lol. I enjoy watching each species sleep and wake up since it always varies, but I never think of actually putting it on video, though I was never sure if anyone would find any interest in it anyway.