Can anyone explain this more clearly, in order to understand if the 'church & state' being bandied around is really not true. If it is true, where can the information be located?
Correct.
U.S. Constitution - First Amendment: Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances. Source