Your question contains two slightly different issues; this is an answer only to the more superficial part, about the abbreviations. Hopefully it can help clear up the confusion this part is causing, and allow more focus on the more substantial issue, about the content of the degrees.
The degrees you describe as “just an M”, like MMath or MPhys are not usually thought of that way, hence the confusion in comments. MMath is short for “Master of Mathematics”, just like MA is short for “Masters of Arts”. Neither is “just an M” — they’re both an M of something. The difference in the abbreviations is because for historical reasons, Master of Arts and Master of Sciences are used for degrees in a wide range of subjects, and so are very common, and have shorter abbreviations; where as Masters of other subjects have to provide a bit more of the subject name in order to be intelligible.
So the other half of your question can be rephrased as: what typically are the differences between programmes called MA, and programmes called Masters in Subject — e.g. between an MA programme in a mathematics department, and an MMath programme?