Are these courses 3 or 4 years long? If they are 3 years, then they're most likely undergraduate degrees, and like somebody mentioned, the title MA just comes from tradition. 4 year courses leading to an MA or MSc are normally known as "undergraduate masters". You can normally choose to graduate at the end of 3 years with a BA degree, or carry onto the 4th year to get an MA without a BA.
If you want to do a postgraduate masters instead of an undergraduate one, it's still one year after getting your BA, but these courses are normally a lot more expensive with little funding opportunities. With an undergraduate masters you can still apply for student loan in your 4th year. Postgraduate masters courses are normally full 12-months long without summer holiday, whereas undergraduate masters have the same term time as a normal undergraduate degree. There are normally 2 types of postgraduate masters: taught or research. Taught masters cover basically the same syllabus as undergraduate masters, while research masters give you a chance to work on 2 or 3 research projects, normally one after the other.
I hope this wasn't too confusing! Oh and this is based on my field, so it may be slightly different for Psychology.