I'm going to start building an electric car soon, and i'm trying to understand everything about ac and dc motors, how they work, and which application would be best.
There are many different types of AC motors. Very few of them have permanent magnets inside. An AC motor with permanent magnets is called a permanent magnet synchronous motor. A brushless DC motor is essentially the same thing as a permanent magnet synchronous motor. A brushless DC motor has an electronic commutator that can be an external controller or circuitry inside the motor. The electronic commutator converts DC power to a square wave approximation of AC.
Since the power is going to be supplied by dc batteries, the motor should be dc. The reason is clear, you need all the efficiency possible. By use of an ac motor you would need a power-robbing inverter. I don't know of any ac motor with a magnet, there are always coils on the stator and rotor. DC motors have the magnets and brushes are being phased out. So, the best way to go would be a brushless dc motor. They may cost a bit more than the brush motors, but well worth it. You'll never have to deal with noise and cleaning the silly things.
Most do not. Some AC servos do, but generally speaking AC motors use the induced magnetic field in the stator generated by a field coil. This is why they are called induction motors. Most large DC motors do not have magnets either. they too use field coils. but some small DC motors do have permanent magnets.