The real deal

Although many classes claim to be teaching taijiquan, very few are.
In order for the Art to qualify as taijiquan, it must adhere to the essence of the Art:

1. Move your body in accord with The Tai Chi Classics 
2. Train all 13 areas of study
3. Follow Yang's 10 Essentials
4. Maintain medically-sound body use
5. Functionally apply the Art in a skilful 'taijiquan' way
6. Employ the taijiquan principles at all times
7. Embody the teachings of Taoism
8. 13 energies should be made manifest at all times
9. Every movement is a whole-body movement

Providing these criteria are met, you have an immense degree of freedom for personal expression and individual interpretation.