Dave,
The picture you linked shows a complete Semco system, including the muffler itself, the black adapter, and the strap. The part number coding for the adapters includes both a color and a part number. The Veco .19 adapter I linked above is in a pink package and marked 6-S, with S meaning small. The adapter you sent is in a blue package and marked 4-L, meaning large.
It's possible that some Semco mufflers may happen to fit directly, without an adapter, either by chance or by design, but the adapter system was the primary design thrust.
Peter