DWP letters are rarely informative, so I would be cautious of reading too much into the fact that it appears to be worded differently.
To be placed in to the Support Group you need to meet one or more of the SG Descriptors, this is the same for everyone.
You don't say when you were placed in the SG, but there is no time limit to request the ESA85A, just call the DWP office that deals with your claim and ask for a copy, we recommend following up the request in writing.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems