Hank, your stairs will be red oak, if they are oak. There are really only 2 varieties of oak sold, red and white. Red is much more available so they will use that for something like stairs. The moldings you are considering will be red oak for the same reason. This said,it can be difficult to tell between them, particularly on small pieces.
I am working on some glue-up, cut from the same (red) oak board, and they can look exactly the same on three sides and like they came from a totally different tree on the fourth. That's just the nature of wood.
I still don't have a good picture of what you are describing but it sort of sounds like your builder applied moldings to your stair treads and I have seen that done to hide the end grain. You should be able to remove the old molding with a good sharp chisel (watch for nails). Work gently back to the joint between the tread end and the molding by splitting the molding long ways. Work carefully back to the old glue joint. Then cut the new moldings to length, glue, drill for nails and nail. Sink the finish nail heads and fill the holes.
It is impossible to tell about matching the finish without looking at it, but you might think about putting masking tape on the old wood and staining the new. Apply a coat or 2 of finish to the new wood, sanding between coats, then remove the masking tape, sand all the stairs and apply a last coat of finish over the whole thing. But that's just my best guess without seeing it. As far as color matching and what kind of finish to use, I will not even try to guess.