Final answer:
The Puritans of Massachusetts Bay aimed to reform the Church of England from within, while the Plymouth Pilgrims separated from the Church, believing it couldn't be reformed.
Step-by-step explanation:
The Puritans of Massachusetts Bay and the Pilgrims, or Separatists, of Plymouth had contrasting views regarding their relationship with the Church of England.
The Pilgrims of Plymouth were labeled as 'Separatists' because they believed that the Church of England could not be reformed from within and thus, they sought to completely separate from it.
Conversely, the Puritans of Massachusetts Bay held the view that the Church of England could be 'purified' of its Catholic elements and reformed, rather than abandoned entirely.
This fundamental difference in belief is what distinguished the two groups, despite them both wanting to practice Calvinist-based Protestantism without persecution.