True or false buddhists and hindus worship the same gods?

Yes they do with some slight variations. The Buddha lived some 500 years before the Common Era, a time in which the Purāṇas were still in a rudimentary phase. The Buddhists texts thus do not mention the Purāṇic deities but frequently refer to the Thirty-three gods of the Vedic Pantheon.

The Buddha was supposed to have met with them all and preached the Dharma to them.

After his enlightenment he was actually reluctant to go out to preach but was encouraged to do so by Brahma.

Buddhist devotional texts invoke the blessings of all the Buddhas and the Devas - the 33 aforementioned ones.

Explanation:

i confess that there are several parts of this constitution which i do not at present approve, but i am not sure i shall never approve them: for having lived long, i have experienced many instances of being obliged by better information or fuller consideration, to change opinions even on important subjects, which i once thought right, but found to be otherwise. it is therefore that the older i grow, the more apt i am to doubt my own judgment, and to pay more respect to the judgment of others.

social contract theory, nearly as old as philosophy itself, is the view that persons' moral and/or political obligations are dependent upon a contract or agreement among them to form the society in which they liv