The major difference, really the only difference, is the type of joinery that is used. A timber framed building uses traditional joinery, like mortise and tenon, dovetails, and tongue and fork (to name a few) to form the connections.The mortise and tenon joint is used to make the majority of timber framed connections and has been the basis for timber framed projects since the very beginning.
Post and beam construction has a very similar aesthetic, and the joints can look similar, but the stark difference is the connections are simple, sometimes made with plates and bolts. Some post and beam projects are done without the plates. For those projects, the connection is made by lag bolting the timber components together.
There is no doubt that steel can bring a lot to the table when it comes to the design and overall concept of a frame, especially when someone is trying to marry a rustic look with an industrial look. Self-builders often use steel as an aesthetic component of a frame. There is no right or wrong when it comes to the concept and design of your timber frame project. Everyone has different tastes.