A HELOC and a home equity loan are second liens: they sit behind your existing first mortgage and leave its rate and term alone. A cash-out refinance does the opposite — it pays off the first mortgage and reprices the entire balance at today's rate. When your current rate is well below market, that repricing is usually the largest cost in the decision, and it is invisible if you compare quoted rates alone.
Between the two second liens, the difference is shape rather than kind. A HELOC is revolving and typically variable — right when funds are needed in stages, as in a phased renovation. A home equity loan is a fixed lump sum with a fixed payment — right when the amount is known and payment certainty matters more than flexibility.
Qualification is a separate question from structure. If you are self-employed and your returns understate what the business produces, a bank statement path may reach the equity your tax returns will not. If the property is a rental rather than your home, DSCR financing qualifies on the rent instead.