I think that position could blur the distinction, but the two types of mate are not the same thing. Here's an Anderssen's mate with no restricting pawn:
And here's an Opera mate with no bishop along the long diagonal:
So, while the two are different, in some cases I guess they can overlap.
(1) Chess definitions are typically poor and contradictory. I've posted a number of threads asking about similar definitions.
(2) Mate types overlap.
(3) Wikipedia is full of inaccurate descriptions, especially on chess topics.
(4) Position definitions often do not take into account lines of force or pieces having the same effect as pawns, such as a back rank made being possible if one of the three "pawns" directly in front of the mated king is a rook.
It appears that the definition of Anderssen's Mate is broader than that of an Opera Mate since Anderssen's Mate allows the queen *or* rook to be supported by a pawn *or* bishop (https://www.chess.com/article/view/mating-patterns-7-anderssens-mate), so I believe the postion you posted falls into a category overlapped by both definitions.
(3) Wikipedia is full of inaccurate descriptions, especially on chess topics.
Yes, Wikipedia chess pages have inaccurate information. I will edit them as soon as I can.
Is this an Anderssen's mate or Opera mate?
According to Wikipedia, Opera mate uses losing's side pawn to restrict its own king. In this position, f7 fulfils that requirement.
But it also fits the description of Anderssen's mate.
I fail to see the difference between Anderssen's mate and Opera mate except for the blocking pawn.