Smothered Mate or Not? - Chess Forums

Is this considered a smothered mate or not? I was "called out" in another forum for referring to this as a partial smothered mate (I don't know if such terminology even exists) and not just simply a smothered mate. My reasoning is that there is an empty square adjacent to the checkmated king. The typical

In chess, is it possible to end up with a stalemate wherein the King is

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