Take a look at the following text taken from "Logical Chess" by Irving Chernev. What are considered the squares a piece attack? How are the queens attacking 9 compared to 5 and the bishops 13 compared to 7?
Chernev is using the word "attack" to mean the squares that piece could move to on the next move. That includes empty squares and squares occupied by enemy pieces. He clearly feels slightly ambiguous about his usage because he also uses the word "control" to mean the same thing when talking about the bishops.
So, for the black queen:
- it can move to b8, c8, d7, d6
- it attacks the piece on e5.
That makes a total of 5 squares it is also protecting pieces on additional 5 squares.
For the white queen:
- it can move to e1, f1, d2, d3, e3, f3, e4, g4, h5
- it is not attacking any black pieces
That makes a total of 9 squares. It is also protecting pieces on an additional 5 squares.
The same calculation can be made for the bishops. The point Chernev is making, before the days of engines, is that white's pieces are more mobile. They can go to more squares. Nowadays engines often use that kind of measurement to make small adjustments in the values it assigns to the pieces but it featured in the evaluations of top players long before the era of engines..