1) Yes. Brushless can also include induction motors, but generally when someone says "brushless" they generally mean "brushless DC" which is a specific flavor of synchronous machine.
For whatever reason, the BL stands for BrushLess, and DC in this case means it 'runs on DC voltage, vs a BLAC motor, that runs on AC. So both BLDC and BLAC motors could be referred to as brushless motors.