https://malegislature.gov/Laws/GeneralLaws/PartI/TitleXX/Chapter140/Section131
MA laws states a Class B does not allow for the carrying of a concealed firearm. For class A it doesn't state it is illegal to carry it concealed so it is allowed. Like was stated law mostly tells us what we can't do. If it is restricted then it is legal.
(a) A Class A license shall entitle a holder thereof to purchase, rent, lease, borrow, possess and carry: (i) firearms, including large capacity firearms, and feeding devices and ammunition therefor, for all lawful purposes, subject to such restrictions relative to the possession, use or carrying of firearms as the licensing authority deems proper; and.......
(b) A Class B license shall entitle a holder thereof to purchase, rent, lease, borrow, possess and carry: (i) non-large capacity firearms and feeding devices and ammunition therefor, for all lawful purposes, subject to such restrictions relative to the possession, use or carrying of such firearm as the licensing authority deems proper; provided, however, that a Class B license shall not entitle the holder thereof to carry or possess a loaded firearm in a concealed manner in any public way or place;