How to determine the reason for unconsciousness?

Can visual inspection tell the reason a creature is unconscious? Is there a difference between a creature that is sleeping normally, sleeping magically, or unconscious due to dropping to 0 HP? Does a stable creature at 0 HP look or behave different to an unstable one?

This came up in game last night after a character in darkness cast sleep on themself. Another character moved to the unconscious figure. The player said “I shake them awake”. My question was, “How do you know they are sleeping? They might be at 0 HP, in which case wouldn’t the appropriate action be to use Lay on Hands?” The player knew what had happened but all the character knew was that they moved to within darkvision range and saw their friend unmoving on the ground.