After buying a home I was redoing the fireplace to make it a bit more modern and in doing so lost a side of trim that surrounds the boarder of the tile.

You can see the right edge is missing. I figured this would be a quick fix. Though I wouldn't likely find the exact color, I could buy a long piece for trim, stain it to a similar color, make some 45 degree cuts, put the new pieces back in. When browsing my chain department stores I didn't quite find what I was looking for. I ran into hardwood floor reducers. They look like so...

But the edge I have around the hardwood floor and the tile looks like this...

The reducers I saw had gap heights of about 1/2 in. while the pieces I have going around my tile are 1/4".

Just curious if I should be looking for a different type of precut piece and that a reducer is not what I should be searching for. The pictures in the hardware stores showed the reducers going from wood to wood (not wood to tile), and also have a metal runner they screw into, which is why I feel I might not be looking for the correct name of trim. Is the boarder that I had around the tile more likely to be a custom piece? I am limited in tools at home to make the proper adjustments other than a miter(mitre?) saw box with saw and an oscillating multi tool.