Roger Williams himself was a Puritan. He was the founder of the state of Rhode Island. Williams was also known for his advocacy in the separation of church from the state. Therefore, his ideas differed from other Puritans although he himself was a Puritan.
In comparison with Puritanism, Williams embraced the Baptist principles and radical ideas like "soul liberty" which he claimed that no one could identify which religion is the true one. These ideas made his banishment from Massachusetts.
Except these ideas, his approach was the same towards Puritanism. He was a Puritan priest and he moved to the New World like other Puritan leaders.