Why does fish stick to a pan which is not very hot?

Have you heard of the leidenfrost effect? If you drop a bit of water on a very hot pan, the water floats around on its own cushion of steam, thus not touching the pan at all. Similar things happen when you sear meat on a pan. The steam keeps the food from bonding with the pan.

In general you shouldn't cook meat on a medium heat. Generally you want to cook meat either on a screaming hot pan/skillet with a heavy bottom, or low and slow. Rarely in between.

I have no science to back this up, but watching a documentary on Francis Mallmann, who cooks over wood fires, claim that when the meat first touches the grill it sticks, but once the Maillard reaction occurs the meat begins to unstick. He says he hates it when people touch the meat and move it around, and that its best to just leave it be until its ready to be flipped. People associate cooking things very hot with burning them. But in reality getting a nice sear requires very high heat, which creates many of the flavor compounds in the food we eat. You're more likely to burn or overcook something at a lower heat, because you're cooking out all the moisture slowly then it begins to burn the entire thing very rapidly, rather than browning the outside. Which could also make the food stick to the pan.