According to chesstempo.com:
The Opera mate occurs when the opponent king is mated on the edge of the board by a rook placed on the edge next to the king, and a bishop supporting the rook, and blocking escape onto the bishop's diagonal. A piece friendly to the mated king (usually a pawn) is blocking the king's escape on the diagonal of the colour opposite to the supporting bishop.
So it's saying the Opera Mate can occur anywhere along the edge which would make Anderssen's Mate, which does require the mating-rook to be in the corner, just a special case of the Opera Mate.
If you buy the chesstempo defintion, then just because Morphy's Rook was at d8 and Count Isouard's King was at e8 and a pawn blocked the escape doesn't mean it can't happen anywhere along the edge as long as it's the King's own piece or pawn that prevents the King's escape.