They are both steeped in what we would call philosophy and theology."
Granted, but remember that Jefferson and other Enlightenment figures were devoted to what they called "the laws of nature and of nature's God".
For them, "natural law" and the ethics on which it is based could be derived from nature, without reference to the Bible.
No, Jefferson was not strictly a Deist, "Christian-deist" would be a more appropriate term, along with "Unitarian", as understood in those days.
In another (1803) letter to Priestly, Jefferson explained that his interest in (basically) a Deist's Bible came from his 1799 conversations with Dr. Benjamin Rush.
What Jefferson wanted was to emphasize the "principles of a pure deism" taught by Jesus, while "omitting the question of his deity".
Indeed, it seems that many of our Founders were uneasy, if not outright uncomfortable, with the Deity of Christ.
Regardless, Jefferson did not abandon the Bible, or "nature's God", but he did want them strictly, ah, suborned to his own naturalistic outlook.