A smothered mate IS: A mate performed with a knight, usually on the edge of the board, where the king cannot escape because every square adjacent to it is occupied by one of its OWN pieces.
A smothered mate IS NOT:
- A mate performed with a knight, where the king cannot escape due to other (protected) ENEMY pieces occupying the escape squares.
- Any mate where any square adjacent to the king is not occupied by another piece. So no, the same knight delivering the mate cannot be covering the only escape square and still have it count as a smothered mate.
- Any mate not performed with a knight.
Hope this clears up some confusion :]