Called the school and figured I would post the info so if anyone else is looking they don't have to ask.
The mmd is just an id card that shows you have had a background check and is not related to the stcw. It sounds like the DHS also has an id card though I am not sure if you need it or not.
stcw certification starts with the BST basic safety training. The other ones: AFF,BRM,AB and MROP are just specialized training from the BST course and are generally needed for a specific job you would be doing aboard a ship. Except maybe the MROP.
Chapman only offers the BST every 3 months as it dovetails with their PMT course so the graduates can take that cert right away. So now I am looking at rearranging my life in the next 3 days so I can go take the BST next week.
good thing I don't have kids...
Detail here USCG National Maritime Center - STCW - Certification for Unlicensed Personnel
and Chapman School of Seamanship - Career Development & IMO Compliance