I completely agree with you in the big difference, I am not arguing with you on that. To put Jefferson's Bible as a historical explination of some dude that was good, is not entirely correct though.
Jefferson had issues with Churches in general. He didn't like how they all competed with each other, and would demolish the competition if they had the power. To him religon was a personal issue, not something to congregate and try to claim 'mine is better than yours'. It has been stated in a few books* I have read that he was closer to Unitarianism (which is a type of Christianity), but didn't become part of the church due to his distaste for congregating people for religon... but he spoke very highly on the church and hoped it would become the next large church, if there were to be one.
He was not 'Christian' in the usual sense of the word, but he believed in much of the core of Christianity (one God, Jesus as a role model, and many other things similar to unitarians).
"To the corruptions of Christianity, I am indeed opposed; but not to the genuine precepts of Jesus himself. I am a Christian, in the only sense in which he wished any one to be; sincerely attached to his doctrines, in preference to all others; ascribing to himself every human excellence, and believing he never claimed any other." **
*American Sphinx - Joseph Ellis **Essential Thomas Jefferson (A collection of letters written by Jefferson) and a few others I can't remember at this time