Each version has its place and none can be said to be the only way. Lets examine them one by one.
1. Sliding Taan Sao
Firstly lets understand how linear movement is achieved. As Taan Sao normally is considered linear.
Three main muscle groups are needed to complete the Taan Sao movement.
1) The shoulder represented by the circular path on the image to the left with 1, 2, 3 labeled.
2) Also Triceps represented by upper curve.
3) Their are also chest muscles acting on the elbow position, pulling the elbow towards the middle of the body.
The wrist should travel in a linear line from when the elbow reaches points 2 to 3. This is achieved by timing both the shoulder and Triceps extension.
So the effect of what appears to be a straight line that the palm travels on is really a complex set of timed moves with groups of different muscles. This type of Taan Sao is used mainly against high round attacks. It's deflection comes from the angle applied and slides over the oncoming punch.
There's not a great deal of movement with Taan Sao normally as your guard position would have the arms in front of the body. Round punches can generate a lot of momentum.
So how does Taan Sao stop the attack?
Because Taan Sao does not oppose the attack on the exact opposite angle it does not have to equal the on coming energy. The attacking energy is dispersed over time as it it forced to redirect or slide on a downward angle. With your defending elbow being driven from the middle of the body, your whole body mass assists in stabilization of your technique, whereas the opponents round punch has only the momentum energy. As it slows down there is little stability.
2. Rolling Taan Sao
Rolling Taan Sao may seem similar to sliding Taan Sao, but its purpose is very different. Its defense is against high straight punches, and deflects from the side of the attack by rolling the palm as it travels forward. There are two angles to consider when using Taan Sao.
This angle is more important when applied to the round punch, as it determines the amount of deflection as it travels over the attack. But when applied to the straight punch it is not just this angle that initiates the deflection, the roll of the palm moves the straight punch across while the angle of the technique moves to its final point.

2) The angle the technique in regards to the attack.
This is the minimum angle for which a rolling Taan Sao can deflect an oncoming straight attack, but the defense has to be just to the side of the punch. Because the attack spends most of its energy in a forward direction, it doesn't take a lot of energy to move it across as the punch is still able to extend.
3. Reverse Taan Sao
Reverse Taan Sao is an efficient deflection when applied from an extended arm position. Used mainly against high straight punches. It may be that you initiated an attack, your opponent also punches over your arm at the same time, your arm is not in a suitable position for a normal Taan Sao as it is extended past its normal position. The reverse Tan comfortably deals with the attack.
4. Flipping Taan Sao
With flipping Taan Sao the starting point is across the body. This technique uses speed and momentum to flip over the top of the attack. This technique is certainly the most aggressive of all the Taan Sao's used, but under certain circumstances extremely efficient. Applied against high straight punches or to create an opening. Footwork must be applied otherwise you will open your centre.
Contact area
The surface area used by the Taan Sao varies with the Type of Taan Sao used.
The surface area used by the Taan Sao varies with the Type of Taan Sao used.
Sliding Taan Sao contact areaRolling Taan Sao contact area

Reverse Taan Sao contact areaFlipping Taan Sao contact area

Summary
It is certainly possible to make any one of the Taan Sao's shown to work for other circumstances. In this way if you are shown flipping Taan Sao against round punch or sliding Taan Sao against straight punch and so on it does not mean they are wrong. It comes down to where you spend your time training, you can make virtually anything work if you train hard enough. On the economy scale though it may be worth looking at the different ways that a technique is applied, and if nothing else at least you can understand the mechanics behind them.
Kudos to KWCKF.
It is certainly possible to make any one of the Taan Sao's shown to work for other circumstances. In this way if you are shown flipping Taan Sao against round punch or sliding Taan Sao against straight punch and so on it does not mean they are wrong. It comes down to where you spend your time training, you can make virtually anything work if you train hard enough. On the economy scale though it may be worth looking at the different ways that a technique is applied, and if nothing else at least you can understand the mechanics behind them.
Kudos to KWCKF.
