For faculty positions: Cover letter vs. a letter of application
Cover letter = letter of application.  It typically goes: "Hi, this is who I am, this is where I got my PhD, I have published here.  Let me tell you a little about my research.  Let me tell you a little about my teaching.  I want to join your faculty because of this reason.  kthxbai"

It should be two pages, single spaced, maximum.  Use letterhead if you've got it, but keep in mind that letterhead is only used for the first page; the second page, if you have a second page, is on regular paper.