The score difference could be caused by several reasons. I can't recall who underwrites Old Navy but some CCs do use their own internal score when calculating credit risk. GE-backed cards, for example, have a max score of 620 or something like that. You might be comparing apples and oranges. Assuming for a second that it is a FICO score, it could be a CC-enhanced FICO score which scores your CC-experience moreso than any other account and comparing a Classic FICO like on here or the free one via Wal-Mart could produce very different results. Did Old Navy list a score range? That can help pinpoint what they used.
Even if a collection is paid, lenders and FICO still view it as if it were unpaid. In terms of FICO, it doesn't matter if you owe $10k or $0, the damage is equal. Try sending a GW letter.
Per the loan comment, it really doesn't matter per FICO. You can hit into the 800s without one. However, some lenders have their own criteria and maybe that's what they are looking for. I certainly wouldn't rush to get one though. I bet if you cleared their other comments then approval would come without a loan reporting.
Old Navy is backed by GE as well. Considering you got approved for a Walmart card that is odd.
I thought Target Visa was discontinued for new apps. Is it back?