Flame is the chemical interaction between gases, resulting in light and heat. When a combustible material is heated to a specific temperature it will begin to decompose and turn into a gas, at a certain temperature specific to the material the gas will ignite producing flame. This is known a pyrolosis.
Heat is a form of energy and can reach temperatures in excess of 1000 degrees centigrade.
Flame can spread by touching other materials causing them to pyrolise and ignite. Flame can also raise the temperature of other adjacent materials without touch by RADIATING its heat to cause further fire spread, although the main means of fire spread in Buildings is by the medium of smoke (see flashover).