This documentation assumes knowledge of channels. And terminologies are for Foundry Nuke; as same operation have different names over different packages, but the work is same.
Multiply multiplies each channel information of one image to another. The result is subtractive as we multiply..
Plus adds pixel value from background to the foreground.
The screen is a conditional operation. It multiplies if pixel if higher than 50% threshold and plus if the value if the value if lower than 50%.
Average averages the range between both pixel channels. Mathematically A+B/2 (B=background, A=foreground).
Min and Max keeps minimum and maximum per pixel value from both the images.
We can group above operation in one group and call it commutative. The operation in this group does not affect the result if background and the foreground are swapped, the result will be the same.
Over as the name implies, puts foreground over the background. Pixels are overwritten over the background.
Minus subtract foreground pixel from the background pixel.
This one is like minus, just it subtracts background pixel from foreground pixel.
Divides foreground by background. A/B else 0.
Matte is just like premultiplying foreground with its alpha. Otherwise it’s just over.
Helpful in checking the difference between two states if comp.
Overlay is not to be confused with over. It multiply if B<0.5, screen if B> 0.5. Hard-light is with input swapped.