I just received a phone call from a Christian friend of mine inquiring about the reason that Islam prohibits sleeping on your stomach. I explained to him (as per my limited knowledge and please excuse me if I am wrong) that the Prophet Mohammed (peace be upon him) stated that it is preferred if you sleep on your right side.
The medical rationale (and this is only conjecture as I am a layman) is that sleeping on your left side places too much pressure and stress on your heart. Sleeping on your back causes you to snore and I do not know what sleeping on your stomach does (as I am not a doctor) :-) Thus, it is preferred to sleep on your right side but it is not prohibited to sleep on another side.
He stated what is the difference. The Prophet Mohammed (pbuh) was a role model for Muslims and we aim in our quest to become better people by emulating him and his actions. Thus, there are things that are directly prohibited in our religion (ex. drinking alcohol, cursing, etc...) where if we do them, we acquire sins. Meanwhile, there are other things that are preferred to be done and if we do them, then we acquire good deeds in our book, but if we do not do them, then we do not acquire sins. An example that is relevant during Ramadan is the Taraweeh prayers.
Hope that the above explanation will suffice to those of us that aim to educate non-Muslims about our religion.