Matching colors with tinted Polyurethane

There are a variety of ways to make wood look a different color.
The easiest / least potentially blotchy would be to use a one-step finish like Minwax^® Polyshades^® which is a tint added to regular Polyurethane - so the poly itself has tiny flecks of pigment suspended in it. The more coats you use, the darker the color and the more grain obscuring / muddy the coating is. But, sometimes that is a bonus in certain situations.
The picture is of two pieces of molding for around a doorway, one a finished piece, the other with all the blotchy patches of color is the back side of another piece of molding that we used to try to match colors. Using the back side of a piece of the same wood makes a lot of sense. If you are careful and don't slop any finish onto the good side, you can use the wood. Plus, using the hidden side for color matching means that the wood will accept the finish identically, assuming that it is sanded to the same level as the front.
There are a bunch of different colors available (from a bunch of different companies) but it will be rare to get a perfect match right out of the can. If you are trying for a great color match, you are going to have to get into blending. This is where it pays off to buy a number of the same types of finishes, by the same manufacturer. I think you could probably mix and match from different companies, but you are pretty much guaranteed of a good application by staying in the same family of products by the same company.
We had a few different cans from a previous project, and purchased the two closest color matches... ...which weren't close enough.
The secret to being able to make a good sample / good application is to blend enough to do the entire job, rather than trying to eye-dropper / measure out and mix for a sample strip, and then trying to match the eye-droppered sample in a larger quantity. I guess I'm saying to not be afraid to waste finish - mix up enough in-between finishes that you can completely color your project. It helps to have some small clean sealable containers to store your various concoctions in. You can try for a wet match, but it is better to wait the full 6 hour drying time. The other thing you will want to do is that if you are trying for a color match in one coat for a product that needs a few layers for the level of shine you are looking for is to clear coat after getting the color you want. BUT, if you are serious about a good color match, you'll have to top coat your sample strip and wait for that coat(s) to dry. Even a clear poly may change the appearance enough to throw your match off.