biologically speaking, what's the difference between sleeping and just resting?
Difference between rest and sleep

There are many factors which describe the difference between rest and sleep. 

Rest

Rest occurs with conscious breathing. This allows the autonomic nervous system (ANS) to rest. The autonomic nervous system belongs to the peripheral nervous system. ANS controls many organs and muscles in the body.

In most situations, people do not know about the workings of the ANS since it functions in an involuntary, reflexive manner. For instance, we hardly notice if blood vessels change size. 

This is the same case when our heart beats faster. There are some people who can control some of the functions in the body and can know the heart rate or blood pressure. 

Sleep

Sleep it is a natural state of rest for mind and body. It happens in cyclic pattern. This can be one of the reasons to describe the difference between rest and sleep. There are four stages of sleep. 

In the first stage of sleep, there is low-frequency, low-amplitude $\theta$ waves. This stage last several minutes before you enters into the next stage of sleep. In stage 2 of sleep, you brain moves into low frequency. In the third stage of sleep, you receive more high-amplitude $\delta$ waves.

During stage 4, the delta waves account for more of your brain activity and then they return back to stage 1.

Resting is more like being couch potatoes.

Rest is important for health and sleep is a necessary factor. You need both for your physical and mental activity to create energy. When the energy level goes down and wastes increase, there is tiredness and body needs rest. When you take rest, energy is restored. All the waste in the body gets extinguished. Rest and sleep are dependent upon each individual’s ability to relax. If an individual is tensed, he cannot be in the state of rest. Rest is taken to counteract fatigue.

Source: 

[1] http://www.theatlantic.com/health/archive/2012/09/when-you-cant-sleep-how-good-is-lying-in-bed-with-your-eyes-closed/262484/

[2] http://insomnia.ygoy.com/difference-between-rest-and-sleep/