Differences between a suspension bridge with three-hinged stiffening girder and two-hinged stiffening girder?

 What is a suspension bridge?

A  bridge that is suspended using cables which has one main suspension cable and the deck is suspended using suspenders.

Now, the deck is compared to it's length is very slender, so what happens is , when a heavy loads moves from one point to another it tries to change  the shape of the cables something like this:

Now, in order to make sure that of this sort happens we stiffen up the so that even if the load is moving, the girder acts like a rigid piece and does not let this happen. If you are looking for an unstiffened e.g.     take a piece of paper and glue it on two sides with a gap in between and then push your finger you will see it deform drastically. Well the span to depth ratio of suspension bridge is kind of similar and so you require stiffening girder.

Now, in case two hinged stiffening girders,  you have hinges on two ends of the deck, that is on have hinges on two ends of the deck, thath is on pylons. And rest of the deck is hanged by the cables. Because of just two ends conditions giving two equations on each sides, it becomes indeterminate structure to analyse and you have to use a computer desktop to analyse the bridge. 

A two-hinged stiffening girder look like this:

While a three hinged stiffening girder( as you thought correctly three hinged) has one additional in the center just like three hinged arch. 

Now adding one more hinge in the center removes the indeterminancy and you can manually analyse the structure with the tension in the cables. Think of  it as a three hinges funicular arch vs two hinged funicular arch. As we know that  a funicular arch the shape of a cabel with compression member. And analyzing a three hinged arch is much more simple because of the additional moment equilibrium you can take at the third hinge at the center.; the same way, if you invert these structure will let you calculated the force in the cables for the given loads at that location.

Thanks for reading