A roof with a ridge beam can be more easily understood if it's imagined to be a flat surface—like a deck in plan view. The ridge is constructed as a beam that runs from end to end. The ends of the beam must be supported as concentrated loads, generally by posts inside walls or in the middle of a room. The rafters are then connected to the beam and transmit their full vertical load downward. Again, picture deck joists connected to a beam with hangers. The other ends of the rafters bear on the exterior walls.
A ridge board is used in a completely different method of construction. This conventional framing system can be used for roofs with a 3:12 slope or greater and works like a triangle, requiring all three sides and points to be provided, as shown in the illustration. The ridge board merely holds the top point of the triangle together and can be omitted altogether if the tops of opposing rafters are connected with a gusset plate. Unlike a ridge beam, which is structural, a ridge board can be a simple 1-by (3/4-inch thick) that's at least as wide as the cut end of the rafter.
First, there is a difference between a ceiling joist and a rafter tie, terms that many people incorrectly use interchangeably. A ceiling joist is simply a horizontal framing member that runs between walls or rafters to support a ceiling. A rafter tie is a horizontal framing member that runs between rafters to resist the outward thrust of the rafters. The confusion arises from not differentiating the two "objects" from their "functions." A single framing member can, however, function as both a rafter tie and a ceiling joist.
The last roof framing member to discuss is the collar tie, also called a "collar beam". First referenced in the IRC in 2006, collar ties had been required long before that in the Southern Standard Building Code and in the high-wind provisions of the Uniform Building Code. Although many people in the field argue that collar ties are unnecessary, they do resist uplift forces that try to pull the ridge apart (see Collar Ties illustration) in both ridge-beam and ridge-board roof construction.