How does an AC generator produce electricity?

An AC generator works by rotating a coil of wire in a magnetic field. As the coil rotates the magnetic flux through it changes sinusoidally. By Faraday's law the changing flux induces an EMF equal to negative d phi d t which equals N B A omega sin theta. The EMF alternates direction each half revolution producing alternating current.

What is the difference between AC and DC generators?

Both AC and DC generators use a rotating coil in a magnetic field to produce electricity. The difference is in how the output is collected. An AC generator uses slip rings that maintain continuous contact giving a sinusoidal output. A DC generator uses a split ring commutator that reverses the connection every half turn so the output is always in the same direction giving pulsating DC.

AC Generator Simulator — Faraday's Law & El...

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AC Generator (Electromagnetic Induction)