Mor - This is a very formal version of mom and would probably be closest to mother in English. But it sounds like super formal and nowadays no one uses it. (Well, no one I have met has ever used it. Maybe if you live with extremely strict parents or something o_o)
Mamma - This is casual and is just like saying mom in English. (Not the cutsey mama). Most people use this one when they speak to their mom directly. (Once again, from the people I know.) I use this all the time.
Morsan - This is a more slang version of mom and seems to mainly being used when talking about a mom rather than talking to them, though it does happen that in some families they call their mom morsan.