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.
This is the first post of the 2015 repository rerun, which appears to be a good idea. The motivation for this rerun is that while the 12 repositories (go look them up, they're awesome!) exist and people might look them up, few new comments are posted there. In effect, there might be useful stuff that should go in those repositories, but is never posted due to low expected value and no feedback. With the rerun, attention is shifted to one topic per month. This might allow us to have a lively discussion on the topic at hand and gather new content for the repository.
The first repository to be rerun is the Boring Advice Repository, because of... on a whim.
Enter original motivation (by Qiaochu_Yuan):
The Boring Advice Repository is filled with lots of diverse advice, I've summarized some of it in a comment below.
So what should go here? To go with Qiaochu_Yuan again (adding emphasis):
I don't know if you should post new advice here or in the original repository. Perhaps search the old repository with ctrl+f (when on windows) and if you don't get results, post it here.