Nope, Tymer. Let's see if I can explain this.
There are breastplates - they can be either all leather, have elastic inserts or have all elastic shoulders. Most have a wither strap, but some do not.
Elastic shoulders w/ no wither strap:
Then, there are the 5-point breastplates. Because there are 5 points of contact with the saddle/girth.
A breastgirth goes straight across the chest. Some have a strap to keep them in place, when this is used the breastgirth is connected to the billets/girth on each side, like this:
That one is elastic, but they can also be leather:
There are also versions with built in martingales:
Other times they are connected only to the saddle d's, only elastic ones are used this way:
Whew, I think I covered everything :)