@Ben Grubb, it is a bit different in that when done correctly, most of the savings come by shielding your HELOC balance with your income throughout the month so that it doesn't accrue as much interest. Personally, I prefer using the HELOC for a new rental property down payment instead of paying down mortgages as you should make far more money investing in something with a higher return than saving money on a low-interest rate mortgage, but if done correctly it definitely saves money when paying down your mortgage, even without paying extra per month.
The easiest way to show it saves money is to say you only withdraw from your HELOC whatever amount you'd normally spend each month that could be paid with a credit card. For example, let's say you have a brand new 30 year mortgage for $100,000 at 4% interest and that your expenses for the month that can be paid with a credit card are $3,000. You can then withdraw the $3,000 from your HELOC to pay extra against your mortgage and repay the $3,000 with your income as you get paid. The expenses that you would normally pay with your income you would instead pay with a credit card (as much as possible). The credit card won't be due for another month so for all future months you would pay the last statement balance in full with your income meaning your HELOC balance will always stay at $0 and the credit card is always paid before interest accrues. Since the HELOC balance will always be at $0 in this example, you wouldn't ever pay interest against the HELOC amount, but you can go to any mortgage paydown calculator online and see the extra $3,000 payment saves about 1 year and 8 months off the mortgage. However, in this example, once your mortgage is paid off you'd still have the $3,000 debt on your credit card which would take about 6 more months if paying the regular mortgage payment so you'd really only be saving about 1 year and 2 months from the mortgage without ever paying anything extra out of pocket, which may or may not be worth doing this strategy to different people as it requires the individual to consistently repeat the same strategy for every month for many years, something many people won't do.
Most people will withdraw far more from their HELOC than their monthly expenses. I definitely wouldn't recommend this as you increase the risk of your HELOC lender eventually freezing your account, plus I can't see mathematically how you are saving extra money this route as the only savings that I can tell are from shielding the HELOC interest payments by keeping the balance at $0 (or lower than it naturally would be for those withdrawing more than their monthly expenses). However, once again, you'd do far better using the strategy at something that returns a better investment than paying down a mortgage early.