The Sanlun school, also known as the Three Treatise school, is one of the main schools of Chinese Madhyamaka Buddhism. It emerged during the 6th century in China and was heavily influenced by the Indian Madhyamaka school founded by Nagarjuna. The main differences between the Sanlun school and other schools of Chinese Madhyamaka lie in their interpretations of Madhyamaka philosophy and their approach to the concept of emptiness.

One of the key differences between the Sanlun school and other Chinese Madhyamaka schools is their interpretation of the concept of emptiness. The Sanlun school follows the Madhyamaka philosophy of Nagarjuna, which asserts that all phenomena are empty of inherent existence. However, they also emphasize the concept of dependent origination, which states that all phenomena arise in dependence on causes and conditions. This differs from the other Chinese Madhyamaka schools, which tend to focus more on the emptiness aspect and view dependent origination as a secondary concept.

Another major difference between the Sanlun school and other Chinese Madhyamaka schools is their approach to the use of logic and reasoning. The Sanlun school places a strong emphasis on the use of logical arguments to support their understanding of emptiness and dependent origination. They believe that through logical analysis, one can arrive at a correct understanding of reality and overcome delusion. This differs from other Chinese Madhyamaka schools, which place more emphasis on meditation and intuition as a means of understanding emptiness.

Additionally, the Sanlun school differs from other Chinese Madhyamaka schools in its understanding of the relationship between emptiness and conventional reality. They believe that emptiness and conventional reality are not two separate entities, but rather two aspects of the same reality. This means that emptiness is not something separate from conventional reality, but rather the ultimate nature of all phenomena. Other Chinese Madhyamaka schools tend to view emptiness and conventional reality as two distinct levels of reality.

Finally, the Sanlun school also differs from other Chinese Madhyamaka schools in its use of the threefold logic of Nagarjuna. This logic, known as the "three turnings of the wheel of Dharma," is used to refute all extreme views and establish the Middle Way. The Sanlun school places a strong emphasis on the third turning, which focuses on the ultimate nature of reality and the concept of emptiness.

In conclusion, the Sanlun school of Chinese Madhyamaka differs from other schools in its emphasis on dependent origination, use of logic and reasoning, understanding of the relationship between emptiness and conventional reality, and use of the threefold logic of Nagarjuna. These differences reflect the unique approach of the Sanlun school to the Madhyamaka philosophy and its interpretation of emptiness.