At the dry-cleaners where I've ever taken my stuff, how the various garments get logged-in determines the charge. The way the clerks do it initially can sometimes get changed by the back room later on, but that can become the basis for an argument.
In any event, a "sport jacket" is definitely not a "windbreaker". I would never expect any confusion there. There have sometimes been confusions about shirt types, but never anything like the jacket type.
I don't think this is a trivial point with respect to DW's invoices. At the moment, if I were a juror, I'd be inclined to disregard all dry-cleaning related evidence. That includes the everything to do with the jacket -- whichever jacket it was.