It's not sleep like ours. They need to rest too. However animals like fish always need to be on the lookout for predators. A fish like a betta can only sleep until it needs to take another breath. I know dolphins only rest half of their brain at a time so they can stay alert and surface for water. However, sharks don't sleep. Betta seem to enjoy having lazy moments.
One time my CT was asleep, and wouldn't wake up. I was tapping on the glass like mad for about a minute before he woke up Dx
I have had my CT, Sushi, for about 4 days and I'm having a hard time getting used to the fact that he sleeps, or rests. He likes to go to the very bottom of the tank and lay on or nosed into the glass rocks down there. It really freaks me out and my husband tells me, I'm being psycho mom. I just worry about my Sushi and would be crushed if he fell asleep and didn't wake up.