When people talk about a wine’s “finish,” they’re referring to the impression that a wine leaves after it’s been tasted. A long finish is often taken as a sign of quality. Finish can refer to the aftertaste, to how long the flavors last until they fade, and also to the textural impact, like if a wine has drying tannins or a crisp finish. The term “length” is used somewhat interchangeably, but it specifically refers to how long a wine’s flavors linger. I’ve heard some people count a length in seconds or minutes, but I don’t know if that’s very useful to folks unless they have a stopwatch in their hands.
When you say “medium-plus finish,” I imagine you’re asking specifically about length. I don’t think there’s anything wrong with simply saying “medium finish.” Some other ways to describe a finish: moderate length, fine length, good length, modest length, lengthy finish or ample length. I also find it helpful to talk about how the flavors persist, last, linger, crescendo or gain momentum.
Those are just some of the terms I use. There are many ways to describe a wine, so the best thing you can do is find a vocabulary that works for you and feels natural when you use it.
—Dr. Vinny (a pseudonym for Tim Fish wine meanderings)