Final answer:
Puritans in Massachusetts Bay upheld Pilgrim society aspects through strict adherence to Calvinism, by aiming to 'purify' the Church of England, fostering a religiously focused community, and setting up a self-sustaining economy.
Step-by-step explanation:
The Puritans maintained specific aspects of Pilgrim society in Massachusetts Bay by adhering to a strict Calvinist theology and by differentiating from the Pilgrims primarily in their belief about the Church of England's reformability.
The Puritans believed that the Church could be 'purified' of its Catholic elements, while the Pilgrims were Separatists who thought the Church was beyond reform.
The Puritans established a Bible Commonwealth where life revolved around religion, economic activities such as fishing and lumbering, and the enforcement of social order through measures like the exile of dissenters and the prosecution of witches during the Salem witch trials.
Through town meetings and communal engagement, they created a self-sustaining community that upheld Puritan religious ideologies and built a strong economy while setting a precedent for self-governance that would influence the future United States.