The attacker plays an important role in the geometrical shape of the double attack. A knight fork, a pawn fork, a rook fork etcetera all have different geometrics that are clearly recognizable. The angles between the attacker, attacking square and targets can differ, and so can the distance to the attacking square.
The double attack is a member of the duple attack family, which means that it has two targets. And that is where matters become a bit quirky, since a target can be a piece, or one of the other tactical themes. Let me show you a few puzzles where the first move is a double attack, but with different targets.
Piece + Piece
Piece + Mate
Piece + Invasion
Piece + Loading a discovered attack
Piece + Deflection of overworked defender
Piece + Coercion into another double attack
Defender + Mate
Defender + Double attack
Only one simple pattern, but totally different positions, with totally different geometrics. Yet we must learn to recognize the archetypical double attack in all these positions. To make matters even more misty, the precursor of a double attack can be any tactical theme. Luckily there are only about 18 important tactical themes.