The name given in birth certificate is different from the name in the school records.What should I do to get a birth certificate which contains the name as in the school records to apply for a passport.

I don't know what the laws are in your country, but I suspect that they are the same is the US: you can't change a birth certificate. You need to contact the school instead, or if the name is just a rearrangement of middle names, try it the way it is first.

What is the difference of the names? Is it a formal difference like different sir names or is it informal such as Johnny instead of Johnathan ?