Woodstove installations can be of several types. One, for free-standing woodstove; another, for fireplace inserts.
Since EPA-certified stoves are a recent phenomenon, there are lots of older, pre-EPA stoves in use including Franklin woodstoves, non-airtight stoves and some that are airtight.
The wood stove industry has made huge technological strides in recent years. EPA emission standards have resulted in new designs for cleaner, safer, more efficient wood burning.