Position #1 is the classic FBI position, light held far from the body, keeps the body from being a target of return fire.
#2 is the position developed by the Surefire institute, illuminates sights an target, minimal body exposure when clearing corners. Head turns, light turns. In another post I made, it's the one I use when wandering with my dog at night.
#3 is the Harries--support and isometric tension for light and handgun
#4 is the Rogers, "cigar" hold--requires a butt activated switch. With a regular Maglite switch, they call it the Chapmann. When the thumbs on the handgun and light are aligned,supporting each other, it's called the Ayoob position.
At least this is what I was told by a MA Law Enforcement Firearms Instructor and Armorers Assoc member during a class. Each has it's place depending on the situation and equipment.