Electric motors, generators and thermoelectric effects

Take a coil of wire, spin it inside a fixed magnetic field, and Faraday's law of induction takes over: the flux through the coil is constantly changing as it rotates, so an EMF is induced with a peak value ε₀ = NBAω — proportional to the number of turns N, the field B, the coil's area A, and how fast it's spinning, ω. That's a generator, and both the frequency of the resulting AC and its peak voltage grow with rotation speed, not just the frequency alone.

Run the exact same device the other way and it becomes a motor. Instead of spinning the coil to induce a current, feed a current into the coil sitting in the field, and the magnetic force on that current turns the coil instead — every generator is a motor and every motor is a generator, differing only in which quantity (mechanical rotation or electrical current) is the input and which is the output. This is why a spinning electric motor, disconnected from its power source, will generate a voltage if you keep turning its shaft by hand.

A thermocouple gets to electrical energy through a completely different door. Join two different metals at two junctions held at different temperatures, and the Seebeck effect drives a small voltage around the loop — no motion, no magnetic field, just a temperature difference converted directly into an EMF. It's a much smaller effect than electromagnetic induction (a typical thermocouple produces only tens of microvolts per degree), which is why thermocouples are used for precise temperature measurement rather than power generation, while generators handle the job of producing usable electrical power.