A photo diode is a semiconductor junction which converts light (photons) into free carriers. Essentially, the light leads to an electrical current when both parts of the diode are electrically connected.

However, an electrical current is typically inconvenient for measurement. For measurement purposes voltages are much more convenient. To convert a current into a voltage one uses a transimpedance amplifier which can also be used to increases the signal level. A photo diode wired to a transimpedance is called a photo detector.

In conclusion, a photo detector is a photo diode connected to a transimpedance amplifier.

There are conflicting definitions of these two ambiguous terms that even most electronics engineers don’t really know the difference. Functionally, they are similar- they detect light. The photodiode would be used with an amplifier to detect low levels of light because they allow a leakage current that varies with the amount of light on them. Photodetectors are simply a resistor that varies in value with the amount of light on it. No amplifier is required. Typically, the photoresistor is slower than the photodiode. You would use the photoresistor, for example, in a lamp to detect when it’s dark. You would use the photodiode when speed is a requirement, for example in a slave trigger for a photo strobe light.

Photoresistors are also about 1/10 the cost of photodiodes.