The former was the secretary for Oliver Cromwell for some time; I understand that he had more political sympathies with the Puritans than doctrinal affinities (though notable among them was strong anti-Catholic convictions), but he was a professed Christian. He started out training for the ministry and decided to be a poet instead.
Donne was an Anglican clergyman. His love poetry became more sanctified after he entered the ministry...still, he was rather eccentric.