The vs. That glorious day

It is not clear to me why That glorious day is drawing nigh and The glorious day is drawing nigh are treated as separate hymn texts. But then, it's also not clear to me which of them is the original. But "that" has many more instances than "the" (except that, in the absence of page scans or full texts, it's risky to assume that the authority assignments were based on fully informed editing). And I think the alternation between (in the seventh line) "Christ, like a comely bride adorn'd" and "A bride adorned, Jerusalem" is considerably more interesting than the initial "The" v. "That". Also of interest to me is the strength of the case for John Leland's authorship. Eliza Snow's LDS adaptation, "The glorious day is rolling on" is also of interest to me. Anybody who can clear any of this up or provide more information, please have at it!