I hired a painting contractor to stain and poly my new windows. He used (2) coats of oil based polyurethane, but after the second coat, the finish was rough on the pine sashes. The oak jams and casing were fine. I asked him to come back and sand and apply another coat to the sashes, which he agreed to do. I was home when he began the sanding, but left before he began applying the poly. When I got home, the sashes were smooth, but the sheen was much duller than the oak, which wasn't the case after the first 2 coats. I am suspicious of the application of a third coat, but he was adamant he applied it. The windows were not tacky when I got home as well. He said the lower sheen was the result of the additional sanding, but wouldn't the additional application of the poly have the same sheen, as well as be tacky?
I hate to be critical of other contractors, but from the clues you have given in your question, I think I know what happened.
First, pine is a much softer wood than oak and needs to be sanded very smooth before the first coat of urethane. The first coat raises the grain of the pine and almost always is somewhat rough regardless of how good the initial prep was. The first coat is sort of a sealing coat and must be sanded lightly to smooth it for the second coat. If the first coat is not fully cured and sanded, subsequent coats will only exaggerate any flaws or roughness. This is what I think happened when you noticed the roughness.
As for a difference in sheen. If the contractor applied the same urethane, semi-gloss for example, the sheen should be pretty much the same as it was before the 3rd coat. They may have used one grade lower sheen. Satin instead of semi, or semi instead of gloss. If you can see any noticeable unfilled sanding marks or really thin coverage, then perhaps the rough surface was sanded with a very fine paper and not over-coated. Oil based urethane stays tacky for several hours. At best conditions, it could be dry to the touch after 2 to 3 hours.
One possibility is that he sanded the 2nd coat and then applied the third coat without adequately cleaning the sanding dust off. Another possibility is that he used too rough a sanding which would produced a lot of scratches in the coat.