Yes, you still own Barclay's the full amount of that zero interest consumer loan. Barcaly financing has nothing to do with the Apple upgrade program, which is financed through Citizens Bank.
Apple's finance plan, via Barclay Bank is a separate program from the Apple iPhone upgrade program, financed via Citizens Bank. In each case you enter into a loan agreement with the Bank, not Apple so you owe the loan back to the issuing bank. If you financed through Apple's partnership with Barclay Bank, then before you can even trade in that phone, you must own it first, which requires you to pay off that loan with Barclay Bank.
One way or another, the bank will always need to be paid back in full for the loan - with the finance deal, that is entirely up to you. On the upgrade program, Apple arranges for the completion and termination of your previous loan (assuming you've made the minimum 11 payments for upgrade eligibility) based on receiving your current iPhone in good working order.