Taijiquan was invented as a martial art, but it is both a good martial art and a good exercise for health, with the latter becoming even better known and perhaps even more important during the last 50 years, especially for senior citizens and for people in the West. Taijiquan is also a performing art, known for its soft, slow, meditative, and fluid movements.
Because of the different focuses and because of its several hundred years of history with millions of practitioners all over the world, there are variations in how the various Taijiquan forms are practiced. This is not even taking into account that there are at least five major Taijiquan styles: Chen, Yang, Wu, Sun, and Wu (a different Chinese word from the first Wu). So even if we restrict our discussion to one particular style for a form set that has been standardized, such as the Simplified Yang Style 24 Forms, there are still variations in how this form set is practiced or taught.
Basically within a particular style, there are two slightly different approaches to Taijiquan: an Artistic approach and a Martial Arts approach. This article discusses examples of differences of these two approaches using the Simplified Yang Style 24 Form to illustrate.
The Artistic Approach places more emphasis on the external appearance of the forms from the eyes of the audience. The Martial Arts approach places more emphasis on the martial effectiveness of the forms from the perspective of the practitioner. The differences are not major, and for novices, they may not see any differences.
The differences are often manifested in the amount of waist (hip) rotation in executing the forms. For example, in the second form “Wild Horse Shakes Its Mane” of the Simplified Yang Style 24 Forms, a Martial Arts approach would rotate the waist more than the Artistic approach. More waist rotation increases the power of the strike by the front arm and the body. For more discussion on this topic, see the article “Importance of Waist Rotation in Taijiquan“. The “Wild Horse Shakes Its Mane” form consists of three similar sub-forms. Relatively speaking, the difference is more obvious between the first and second sub-forms or between the second and third sub-forms. After shifting his  weight from the front foot to the rear foot, a practitioner using the Martial Arts Approach would perform a larger amount of pivot on the front foot so that in his next movement he can rotate his waist more while still striking directly to his opponent. For pictures of this and other forms, see the article “Martial Applications of Taijiquan“.
Another example of more waist rotation in the Martial Arts approach is in the third form “White Crane Spreads Its Wings.” In performing this form, the practitioner using the Martial Arts approach would perform a larger clockwise waist rotation while doing an upward block with his right hand, and then would perform a larger counter-clockwise waist rotation while doing a downward block with his left hand. These larger waist rotations would increase the power of the upward block and downward block.
The fourth form “Brush Knee and Step Forward” illustrates another type of difference between the Artistic approach and the Martial Arts approach. The difference is in the height that the practitioner raises his front leg while doing the brush knee block. An Artistic approach would raise the front leg just slightly off the ground because it may look better in the eyes of many people. A Martial Arts approach would raise the front leg significantly more because the side of the high front leg can provide more protection to the body, i.e., it is better for the opponent’s attack to hit the practitioner’s thigh than his body.
Another difference is in the form “Single Whip.” After forming a hook with one hand, the practitioner turns to the other side, steps forward, and pushes forward with his other hand. The difference is how far forward the other hand is extended before it pushes forward, with the Artistic approach having a larger extension than the Martial Arts approach. A larger extension while turning the body provides a larger arc and may be more aesthetic. A smaller extension would allow that hand to be pushed forward a larger distance and therefore generate more power to that push.
It is important to point out that these are differences of emphasis and in objectives. It is not that one approach is more correct than the other approach.
We end this article by mentioning that for more experienced Taijiquan practitioners, proper breathing is very important. For more discussion on breathing, see the article “Breathing and Taijiquan“. Associated with breathing is the movement of Qi within the practitioner’s body. For more discussion on Qi or Qigong, see the article “The Essence of Taijiquan – Part 2: Perspective from Taiji Qigong“. There may also be differences in the amount of Qi movement between the Artistic approach and the Martial Arts approach to Taijiquan.
 For brevity, we use the word “his” to denote “his/her” and “he” to denote “he/she.”