In short the transistor can be commutated (turned "on" or "off") by pulsing the gate; whereas a Thyristor will begin conducting with a single pulse on the gate and will continue until it is commutated which can be done several ways - one which is when the polarity changes between the anode and cathode which makes it very good for AC. The biggest difference is transistors are usually for low voltage DC and thyristors are usually applied with high voltage AC.
