You're Correct!

Height massively affects the swing type of each player because it affects a players swing plane, or the angle that they swing the club head around them on.

Tall players will have a larger wrist to floor measurement than smaller players. The distance of a players wrist to floor measurement affects the angle that the shaft of the golf club addresses the ball at. Taller players will set the golf club at a steeper angle than smaller players. When a taller player now swings the golf club around them, they will swing at a steeper angle, or on a steeper swing plane. In simple terms, they are wanting to swing the club around them and return it to the position that it started in, so the easiest way and most consistent way to achieve this is to swing the club relative to its start position - or on plane.

To understand swing plane further, take an alignment pole and once you have taken your address position up simply push the alignment pole into the ground so that it replicates the angle that you have set the shaft of the golf club to the ground. A tall player will have a steeper angle with the alignment pole as their hands will be further from the ground and a smaller player will have a flatter angle as their hands are closer to the ground.

To swing on plane, step about one to two yards to the left of the alignment pole, if you are a right handed golfer. Make your swing and ensure that the club head travels up the alignment, at the same angle as it. Not underneath it, or up above it, but directly along it. At hip high your club should make a right angle to the alignment pole and be parallel to both the target line and the ground.

From this position allow the club head to continue up the angle of the alignment pole so that the shaft now becomes parallel to the alignment pole. A taller player in this position will have a much more upright shaft position than a smaller player, whos shaft position will be much flatter.

Returning the club head back down towards the golf ball, the taller player will have a much steeper angle of attack in the club head down towards the ball and they will swing the club head more directly along the target line. The smaller player with the flatter, shallower, angle of attack will have a swing that curves, or arcs, on to the target line more as the club head approaches the golf ball.

As the taller player swings through impact, their follow through will be more upright and the smaller players follow through will be lower and more around them.

Height massively affects swing type as taller players set the shaft of the club more upright than smaller players do. As a result, they have a much more upright swing plane and attack down with a steeper angle of attack on the golf ball. Smaller players make a flatter, more arcing swing that swings through impact with a more sweeping action.

Whether a player has a flat or upright swing depends on the angle that they set the shaft of the club at when in their address position. Taller players will generally have a higher hand position and as such they will set the shaft angle more steeply than shorter players and as such they will have a more upright swing.

Small players generally set the shaft of the golf club at a much flatter angle to the ground than taller players do. As such, the angle that they swing the club head around them on tends to be much flatter or lower and this produces a more arcing swing action than is seen with taller players.