They are just ways to signify the equivalent distortion levels at different parts of a system. Manufacturers claim the best numbers for their products. Ones with gain have the output parameter, ones with losses like passive mixers have the input parameter.
The difference is that for a given IP3 , you have some input power X (Port1), and you
have some output Power Y(Port2). Now how do you want to look at it?
If it's a RX for a SoC and you can't measure Pout directly you might want
to use IIP3, because you can directly measure Pin!
If it's a TX the it would be more useful to use to use OIP3.