Ah, I see. Well, you get somewhat similar financial outcomes but you end up in very different positions.

As far as I understand mortgage offset accounts, the money in that account is yours. You are, effectively, a lender, and the mortgagor -- a creditor. In the HELOC situation when you pay down part of your mortgage, that money is gone. Instead you get a second loan (and a second lien on your house) and now you're the creditor while the bank is the lender. It is not your money.

Thinking about the situation in which your credit rating deteriorates and the bank pulls the line of credit should make the difference between the two scenarios clear.