The relevant letter (e.g. the one containing the words “separation”, “church”, and “state”) from Thomas Jefferson to “messers Nehemiah Dodge, Ephraim Robbins, & Stephen S. Nelson, a committee of the Danbury Baptist association in the state of Connecticut.”

Gentlemen

The affectionate sentiments of esteem and approbation which you are so good as to express towards me, on behalf of the Danbury Baptist association, give me the highest satisfaction. my duties dictate a faithful and zealous pursuit of the interests of my constituents, & in proportion as they are persuaded of my fidelity to those duties, the discharge of them becomes more and more pleasing.

Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should “make no law respecting an establishment of religion, or prohibiting the free exercise thereof,” thus building a wall of separation between Church & State. [Congress thus inhibited from acts respecting religion, and the Executive authorised only to execute their acts, I have refrained from prescribing even those occasional performances of devotion, practiced indeed by the Executive of another nation as the legal head of its church, but subject here, as religious exercises only to the voluntary regulations and discipline of each respective sect.] Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties.

I reciprocate your kind prayers for the protection & blessing of the common father and creator of man, and tender you for yourselves & your religious association assurances of my high respect & esteem.

(signed) Thomas Jefferson
Jan.1.1802.

Indeed, these are undeniably different in any and every sense of interpretation possible:

A.

“separation between Church & State”

B.

“separation of church and state”

Mr. Glen Urquhart, the GOP nominee for the race for Delaware’s lone House seat has attributed the latter to Hitler and the Nazi. Jefferson, you can plainly see, wanted a purely Christian republic on these shores. This is why he used the word “between.”
Adding Judeo to the Judeo-Christian formulation is simply an example of American Exceptionalism and is largely predicated on Jefferson’s own ruthless and unyielding support for the state of Israel. And, of course, there’s always a little Madison in there.

Said it once, will say it many times in the future: the facts do not matter. Plan and act accordingly.