You need not worry about the different birth dates in birth certificate and school leaving certificate. Passport office India has changed some rules in 2017.
According to earlier rules i.e. Passport Rules, 1980, to get a passport, it was mandatory for all the applicants born on or after 26.01.1989, to submit the birth certificate as the Date of Birth (DOB).
After 2017, According to new Passport Rules, there is a list of proof of Date of Birth to be submitted for issuance of Passport.
An applicant can submit any of the following documents as DOB proof, while submitting application for issuance of passport:
(i) Birth Certificate issued by the Registrar of Births & Deaths or the Municipal Corporation or any other
(ii) Transfer/School leaving/Matriculation Certificate issued by the school or recognized educational board
(iii) PAN Card
(iv) Aadhar Card or E-Aadhar having date of Birth mentioned on it.
(v) Voter ID issued by the Election Commission of India
(vi) Driving License issued by the State Transport Department
(vii) Duly attested copy of service record extract in case of Government servants or the Pay Pension Order in case of retired Government Servants by the officer or in-charge of the Administration of the concerned Department
(viii) Policy document issued by the Public Life Insurance Corporations/Companies.
As you have mentioned that your all other documents like Driving Licence, Aadhar Card, School's 10th standard passing certificate etc are having correct (matching) birth date, you can use any of these document as proof of Date of Birth while applying for Passport.
For future or any other purpose, you can also apply for correction in date of birth certificate, on the prescribed application form along with the application fee. It may take some time in receiving of corrected certificate.
However, you can apply for passport with the documents you have with you.
Hope this will help.