I am wondering, is this the same John Cox to whom W. Kelly send so many post cards?

They are not the same person. Kelly's correspondent was, I presume, John Stephen Frecker Cox [1826-1907], see https://www.brethrenarchive.org/people/john-sf-cox/. 'Mr Newton and the Brethren' is by John Cox [1829-1915], sometimes referred to as John Cox, jnr, being the son of a Baptist Minister, John Cox, snr. [1802-78]. Both John Cox jnr and snr were supporters of B W Newton. Timothy Stunt.

Thanks for the explanation, Timothy!