Coaching classes are similar like schools, city coaching classes are more personalized than the school. In a good coaching institute have smaller batches like 20-30 students, to give a personal attention to every one. Best coaching classes have their own strategy to teach their students.
In Private Tuition tutor comes at students home and teaches the student. The price of a private tuition are higher than coaching classes or coaching institutes. In India private tuition are available in different subjects like physics, chemistry, maths, science, english etc.