Any attempt to use a different-looking wood would be very busy and not a good choice. I recommend you get a very good flooring shop to do their best to match the existing wood. They can pull up or cut back existing boards so you can eliminate evidence of the curve.

Are you positive that the wood doesn't extend under the carpet? Otherwise I would agree with qam, have a flooring company patch in matching wood and then have the whole room refinished.

I would replace all of the wood in the curved section.

I agree with the "tie in" (called lacing in hardwood) of more of the same species/cut/width. This would be pretty easy to do. The area of "orginal" hardwood would be sanded down and then refinished at the same time as the new product. This won't do too much to the overall costs as the area infront of the door/closet/stairs is relatively small.

This looks to be red oak in a solvent based polyurethane...it might have a stain on it. It is possible the old finish has turned orange and is giving the wood its colour.