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BrianHere is the link to the auction in question:
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=5243495909&ru=http%3A%2F%2Fsearch.ebay.com%3A80%2Fsearch%2Fse arch.dll%3Fcgiurl%3Dhttp%253A%252F%252Fcgi.ebay.co m%252Fws%252F%26fkr%3D1%26from%3DR8%26satitle%3D52 43495909%26category0%3D%26fvi%3D1
Here are the T206 Museum images of Old Mills to include Browns, Blacks, Southerns, Overprints etc..
http://www.t206museum.com/page/bk_reglt3.html
To answer your question, to distinguish an Old Mill Brown from an OM Southern, the difference is the color on the back. Old Mill Browns are Southerns, but there are also Old Mill Blacks that are Southerns. Difference being brown, black and scarcity.
T206 Museum:
Old Mill is another common back printed in black, and was issued at all times during the T206 set's distribution. There are two different backs. The first advertises Old Mill cigarettes, and was issued with major and minor league players. The second Old Mill back is only found with the 48 Southern League players and specifically promotes the Southern, South Atlantic, Texas and Virginia Leagues. Recently, a few specimens have been found on Southern League players with Old Mill back printed in brown. These brown Old Mill are exceedingly rare and tougher than those brown Lenox variations.
Scarcity order
1. Old Mill (Southern League - Double Overprints) - Factory 649 - District 1 - State NY
2. Old Mill (Southern League - Overprint) - Factory 649 - District 1 - State NY
4. Old Mill (Brown) - Factory 25 - District 2 - State VA
24. Old Mill (Southern League) - Factory 25 - District 2 - State VA
Brian