In the state of Massachusetts, you must have an FID, LTC B or LTC A in order to possess a firearm. Each of these three licenses allows you to possess and purchase firearms but both the LTC B and FID limit you to certain types of guns. LTC A will allow you to possess any firearm that is legal to own in Massachusetts (with the exclusion of automatic weapons for which you would need a machine gun license). Additionally an LTC A will allow you to legally carry a concealed weapon.
If you find that first paragraph confusing, you should settle in, grab a drink and get comfortable because that was the simple part. In Massachusetts, it only gets more complicated from here.
In my classes we do cover the particulars of each license and what makes the most sense for you. Successful completion of either of my classes will fulfill your course requirement for any of the Massachusetts Firearms Licenses.