Not all engines are heat powered motors, and vis versa. I should have clarified earlier as well, but motors convert energy into motion. Engines have a motor, but contain other systems and accessories to aid the motor, and have the potential to create other forms of energy from that conversion process.

Think of an engine as a self-contained package, also known as an assembly. Multiple systems come together to form the engine. You give it fuel, and it converts that fuel into heat, rotational motion, electricity, and cooling. It also lubricates and cools itself. The piston/crank system is the motor component of the engine. The intake, exhaust, and cooling systems are part of the engine, and they allow the motor to keep working efficiently. The alternator and AC compressor are engine accessories.

It gets much easier to understand if you picture other types of engines. In a jet engine, the turbine section is the motor core of the engine. On a steam engine, the motor is the steam piston component that drives the wheels.