I'm not sure the Guild has a position on this so I'll just give you my personal answer.

The two methods have much in common (use of heavy timbers, methods of enclosure, and timber engineering) and differ only in the method of joinery. Timberframing joins the timbers using traditional mortise and tenons (as well as dovetails, housings and the like) and in its purest form uses nothing other than wood to secure the connections. Post and Beam relies on metal (bolts, nails, and metal plates) to secure the joints

As to history; clearly timberframing is the older method -- man had trees before he had steel. My personal theory is that post and beam evolved as a sort quick and dirty timber frame. Most joiners realized that they were spending a large percentage of their time cutting the joinery as opposed to sawing the timbers. Thus, a method that allowed quick interconnection of the pieces would speed up the process. Both methods declined in popularity as a mainstream method with the emergence of sawmills that could produce the dimensional lumber for stick framing. A stick frame is really just a post and beam with very little posts and beams.

Today there is a lot of overlap between the two methods. Many "timberframe" buildings have connections that are secured by concealed steel elements. The result being structures that can meet commercial building codes as well as achieve a higher level of engineering performance (larger free spans and simpler multi-member joints)