What is the difference between a photocoupler and a photorelay?

A photorelay is a kind of photocoupler. A photocoupler consists of an LED at the input side and a photodetector at the output side combined together inside, and a photocoupler product varies depending on the type of photodetector at the output side. Its main varieties include a transistor-output photocoupler, IC-output photocoupler, triac-output photocoupler, and MOSFET-output photo coupler (called a "photorelay").
A photorelay is a device with two MOSFETs connected common-source at the output stage provided with functionality equal to that of a mechanical relay or lead relay. Since the MOSFETs have linear output characteristics in their voltage-current characteristics, this device is distinctive in that it can not only function as a simple switch, but also switch analog signals.