Except PAM stands for "Pluggable Authentication Modules" (as in "PAM Library") - plural. You then write a module for the PAM library, so it makes the most sens

Except PAM stands for "Pluggable Authentication Modules" (as in "PAM Library") - plural. You then write a module for the PAM library, so it makes the most sense to call it a "PAM Module", even if there is some redundancy in the acronym.