The difference between matter and energy is that energy is produced from matter yet has no mass and is the capacity to do work while matter is the physical "stuff" in the universe. Matter needs energy to move.
Lavoisier, in 1789, was the first to list two "substances" that he wasn't sure what to do with. These substances were light and caloric, or heat. Now, it is known that heat and light are not matter, but rather energy. Energy is required by physical and chemical processes in order to work.
Matter can obtain energy in two different ways through either potential energy or kinetic energy. Potential energy is the capacity of matter to do work because of where and what the matters is whereas kinetic energy is the energy that is associated with motion or with what matter is doing.
The Law of Conservation of Energy is useful here as it states that energy cannot be created or destroyed and is therefore only converted from one form into another. An example of this would be heat released on a burning natural gas stove. The heat was originally stored in the compound as chemical energy so it does not leave, but rather changes or converts from chemical energy to heat.