To clarify, these are technical terms for income tax purposes, and are
not defined by any label a bank may put on a loan, such as "HELOC" (home equity line of credit).
Since 1987, whenever you originate or re-finance any mortgage, the portion of the proceeds used to buy, build, or improve your personal residence is called "acquisition debt" (used to acquire the asset), and the remaining portion is called "equity debt" since it is secured solely by the pre-existing equity in the property and is used for anything other than acquisition.
When you re-finance acquisition debt, it remains acqusition debt, but any cash-out from the re-finance not used to buy/build/improve is equity debt. As you pay down principal on the loan, you are considered to first pay off the equity debt, before acquisition debt.