For faculty positions: Cover letter vs. a letter of application In the announcement of a tenure-track faculty opening in computer science in USA, I see a request for


  a letter of application explaining your interest in ⟨university⟩ and in this position


Other documents (CV, research &amp; teaching statements, scholarly work, references) are also requested, cover letter not being among them. The application goes to a small, mostly liberal-art university.

How many pages are typically expected for the letter of application? Is a cover letter expected in addition?

I have read What are the differences between a cover letter and an application letter?, which, however, speaks about a PhD position. I have also read the links provided there, but, they are targeted more towards the non-academic job market.
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.