Secondly, Coxe (the probable writer of section 7 of the LBC) used special terms in the LBC to indicate these truths.
Do you mean paragraph 7? And to which special terms are you referring?
If the authors and signers of the LBC all agreed in 1689 Federalism, and that it was an important distinction, they could have done a better job of explaining it. They wasted no words explaining their position on Baptism and the Church contra Westminster.