The first badge with 'Auxiliary Units' written on is a modern version. The badges were given out at stand down after 1944. Patrols were all meant to have them but were passed to the sergeants of each patrol (patrol leaders) to pass to the rest of the patrol.
Some passed them out, others didn't, some never received them - hence the confusion. It was the only official recognition they received.
The link to the Home Guard is also confusing. Some were recruited from the ranks of the Home Guard, others returned to the Home Guard prior to or after stand down in 1944 and many if not most used the Home Guard as a cover for their training disappearance!
Some were recruited to the SAS and SOE - with quite a few of them giving up their lives. Most however, went back to their daily lives, having signed the Official Secrets Act, without saying a word to their closest family and friends.
You can find out more here:
www.Staybehinds.com and I know there was a specific question about Dorset - here's what we know about the Dorset patrols:
http://www.coleshillhouse.com/dorset...ts-and-obs.php
Cheers
Andy