Purchase more of one of the molding profiles and replace the other to match.

Stop the water leak, possibly from the fridge, then remove the damaged area and replace.

Flooring shows sign of rot.

Yes, choose one baseboard style and then cut the corners properly. :) The one on the left is called ranch baseboard with quarter round, and the one on the right is colonial baseboard.

A Mat, I don't see leak or rot -- only different flooring in the two rooms.

I agree, no sign of a leak in the picture. The ranch baseboard appears to end with a square cut and not a mitered corner. Which ever molding you decide to continue, the existing ranch baseboard pictured will have to be removed and replaced with one mitered for the corner.

Agree with Joseph.