True or false buddhists and hindus worship the same gods?

True

Explanation:

Buddhists are traditionally hard polytheists. Modern Hindus tend to be Monists, because that's the direction their philosophical development would eventually take.

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.