What were the Puritans beliefs compared to Jamestown's?

You've already gotten an excellent answer.  Let me just
add a few more tidbits.

As a whole, the Jamestown settlers
were, in fact, only there for economic gain, despite their claim that they were also
interested in "converting" the "Savages" (Indians).  Only one member of those original
settlers was a preacher, and there were no women in the bunch.  That's a pretty clear
indication that these men came to grab what they could--as they had been sold on the
idea of a "land of riches"--and head back home.  They had no intention of settling or
staying, as is also evident by their lack of foresight in bringing along enough food to
sustain them for any length of time.

The Puritans, on the
other hand, were a mixture of men and women, nearly all committed over the long term
(both in England and in Leyden, Holland, from which they departed for America) to the
principles of faith, salvation, and sharing the "good news" with the natives.  They
weren't persecuted for their faith in Leyden (though their lives were difficult for
other reasons), but they believed they were to come to America to promote the gospel and
evangelize from there to the rest of the world. 

In terms
of this novel, the Puritans of 1692 were rather different than those first settlers in
one important way.  The first group to arrive underwent hardships of every kind and
relied on God for everything--literally everything.  They had little esle on which to
rely.  They were a spiritual people and it showed in everything they said, built, wrote,
and did.  Generations later, life had become much easier and they weren't as reliant on
God as Provider.  Instead, they saw Him more as either Savior or Punisher--and one could
not know which until Judgment Day.  Thus their desire to "root out" sin in an effort to
prepare for that day. In essence, they took over the role of judge here on earth, meting
out punishment for sin without any forgiveness of
sin. 

This skewed or partial view of God and sin and
punishment was, of course, part of the atmosphere which led to the witch trials in
Salem.