am/pm conversion

what is AM/AM conversion and AM/PM conversion in the case of power amplifiers?
the graph Pin vs Pout is also called AM/AM conversion plot. why?

this has been discussed before here:

https://www.edaboard.com/viewtopic.php?t=91681

https://www.edaboard.com/viewtopic.php?t=62224

see also Maas book:
https://www.edaboard.com/viewtopic.php?t=72190
page 15, 416 and 465.