I work on the physical postures (asanas) to develop strength and correct alignment ( this is the fitness input), but with a strong focus on breathing exercises (pranayama) to help to induce clarity of thought, tranquillity and concentration. I also include meditation and relaxation to turn attention inward and help to calm the mind and reduce stress. In that sense you could see it as a sort of therapy, a yoga therapy.
With smooth but intense practice and the appropriate modifications to suit your individual body and mind, yoga can help to aleviate back pain, loosen stiff joints, and also improves depressive moods and depression. It releases stress. In that sense, it is quite similar to an ordinary fitness class, but with a deeper concern for health and well-being.