Matched pairs are typically double guns, usually SxS built to a "Best" gun quality level, built at the same time and "matched" in dimensions, weight, balance and handling characteristics. Also they usually try to match the high grade wood and have a consistent theme to the engraving. They are most commonly English, usually of the "game gun" variety and designed for driven shooting with a gun loader. The purpose is that in the heat of the moment, as you are switching between guns with your loader, you aren't handicapped by having to "adjust" to a different gun.
There are guns built as a set, that are matched in some ways, say wood or engraving, but that are different in dimension or some other meaningful aspect that are meant to be used for different types of hunting, say one for pheasant (longer barrel, tighter chokes) and one for grouse (shorter barrels and more open). Those may be sets but they are not a "matched pair".
People (me for example) sometime will endeavor to make a composed match set by taking two guns and customizing them as much as is required to achieve the same effect. I'm slowly working on a pair of Remington 1894 BE guns with the aim of getting them fairly close. Just for fun. No good reason.