Theoretical physics is the branch of physics that focuses on developing and testing mathematical models and theories to explain the fundamental principles of the physical world. Theoretical physicists use mathematical equations and models to explore the behavior of matter and energy on a fundamental level. They seek to understand the underlying principles that govern the universe, such as the laws of thermodynamics, the behavior of subatomic particles, and the principles of relativity and quantum mechanics.

In contrast, applied physics is the branch of physics that focuses on applying physics principles to solve real-world problems. Applied physicists use the principles developed by theoretical physicists to design new technologies and solve problems in fields such as engineering, medicine, and materials science. They use physics principles to develop new technologies, such as lasers, semiconductors, and superconductors, and solve problems in energy production, transportation, and communications.

While theoretical and applied physics are distinct areas of study, they are often closely related. Theoretical physicists may work with applied physicists to develop new technologies based on their theoretical models. In contrast, applied physicists may use the principles developed by theoretical physicists to improve existing technologies or solve new problems.

Overall, the primary difference between theoretical physics and applied physics is that theoretical physicists focus on developing and testing mathematical models to explain the fundamental principles of the physical world. In contrast, applied physicists use those principles to solve real-world problems and develop new technologies.