Shortest Smother Mate (4 moves!)

it is sort of smother
I agree. I understand that supposedly only a knight can smother mate, but in this case the king is blocked entirely by his own pieces except for where the check comes from. That's awfully close to a smother. If not, I wonder what that mate is called.

it is fools mate
That particular mate is fools mate. But I was wondering what the mate is called when the king is surrounded by his own pieces so he can't escape and the only square that isn't one of his own pieces is on the path of the check.
