Sleep is typically defined by the brain waves activities, delta waves, theta waves, etc., each corresponding to a specific sleep stage. These are physiological markers of sleep. There are also states of "quiet wakefulness" that share behavioral characteristics of sleep, like immobility, for example, but are not sleep per se.

Many "simple animals" like a fly, or a caterpillar or a bee have periods of inactivity that could be an example of rest. But sleep and rest are not the same. If we put brain waves aside, we are left with the behavioral definition of sleep: it is a state of reduced awareness of the surroundings, there will be some latency in arousal, it is reversable, and it is associated either with immobility or at least reduced activity. This study obviously used this definition, so it is not exactly being "tired".