hello shampa Jee, really a nice question asked......
Both the words, Famous and Popular are similar in many ways, only a slight difference. If you ask me, how would you groom your child to be, I would prefer to said..... I choose "Popular" between the two
Both have advantages and disadvantages. Though we earn a lot of money and become a well-known person through the field of arts, sports etc, it is not necessary that he is a nice person in character too. A person become famous merely because of talent. But with virtue one can become both popular and famous. I would like my child to be called a good person and popular and being sincerely liked really by others, than be a famous person, because she can earn it only through the quality she lives in the society. After all we owe something to the society as well and it gives a lot of self respect and self satisfaction also, the most important things of one's life.
Let me give one simple example. One gain easy attention if he becomes famous as an actor or model. What for the case of girls???? Though she becomes famous and have a lot of fans, in mind, our Indians will only say bad about actresses or models. Thousand link ups, affairs and dressing etc... even if she is as clear as crystal. Am I not right? It's not applicable in the case of boys.
So I believe it's easy to become famous than popular and many may use short cuts to achieve that goal, that I never encourage.....