Ok, this post will either clarify things or make them more confusing (let's hope for the former!).

I'll use the ITI numbers for these tartans in order to be precise. You can look them all up at the Scottish Tartans Authority site:
http://www.tartansauthority.com

Tartan No. 2437 is the U.S. Air Force Reserve Pipe Band tartan. The STA notes say:
One of a series of US Military tartans woven exclusively by the Strathmore Woollen Company and adopted by the Band of the Air Force Reserve, Georgia, USA in the early 1990s. Although this has no official US Military recognition, it has been widely accepted by US servicemen and their families with Air Force connections as a representative design.
There have been other attempts to creat unofficial tartans for the USAF, including Nos. 5080, 5075, and 4089.

The Mitchell tartan (No. 3178) was worn by the USAF Pipe Band (unsure if this was the reserve pipe band?) from about 1950, according to the STA notes. This is the same tartan that is worn by the Russells, Galbraiths, and Hunters, and, according to the STA, "acquired the name Mitchell when it was adopted by the U.S.Air Force Pipe Band and renamed in honour of General Billy Mitchell."

To answer another question, no, so far as I can tell the four families that share this tartan have no connection to one another, aside from the coincidence of sharing the same tartan!

Aye,
Matt