A regular snaffle bridle.

All bridles I have ever seen have a crownpiece running across the back of the poll of the head and down on each side, to hold a bit or something replacing a bit. As a matter of fact, I think this would be the basic description of any headstall. If it does not have this, it''s likely something else.

From the bit go the reins into the hands of the rider, for the sake of control of head and neck position, the relaxation of the jaw, and sometimes crudely for the control of speed and direction. These are usually of a length long enough to let the horse stretch the whole neck down to graze.

The browband goes across the forehead and its purpose is not totally clear. There is hardly a risk that the crownpiece will slide backwards without it. It can, however, be nicely decorative.

The throat latch is a part of the crownpiece, and goes around the muscular part of the jaw, and actually serves a purpose:
Should you fall of your horse and he start to back away from you, it will hinder the bridle from being pulled off over the ears. Manege bridles from 1600''s or so rarely have a throatlatch. Those horses presumably never went to battle, and never had to be dragged exhausted through the mud by the equally exhausted cavalry soldier pulling his mount along by the reins. There was no risk of the headstall coming off in the 17th century manege...