You got through an undergrad degree without learning this? My program required electro-mechanical studies.
Anyway, my probably too short answer:
Asynchronous - Induction motors basically. Speed varies with load when used as a motor. Frequency varies with load when used as a generator.
Synchronous - Constant speed motor or constant frequency generator regardless of load. This is why it's used in power systems. Too much load causes instant stall. It also has interesting impedance properties that can be used to tune power grids. Cannot self-start. Needs a kick-start motor.
Alternator - A catch-all term for anything that generates AC power. If there is some definition that is more formal then I don't know it.
dynamo - DC motor/generator. Unlike AC motors, the dynamo's speed can be electrically controlled over a wide range. AC motors tend to have target speed ranges (called a speed-torque curve) and they'll stall outside of their designed operating conditions. Dynamo's are good for variable speed applications. Generally less efficient than AC motors at high throughput but more efficient at very small powers.