For example, let us look at the following chess diagram. It is white's turn. Until now, black queen and rook were safe, but white plays d6! White pawn makes an active attack on the black rook but also opens a2–g8 diagonal, which allows white bishop to attack the black queen (and the bishop is protected by the knight).
The tactic in which one piece moves out of the way of a second so that the second can attack is called a discovered attack (and more specifically a discovered check if it results in check). The piece which moves may or may not move to a position to mount its own attack -- I'm not sure if there's a term for the specific case in which the piece that moves does mount an attack by itself.
You're correct that it's not a fork, which occurs when one piece simultaneously makes two or more attacks. Here you have two attacks but by two different pieces.