Accounting can be fun.
Helicopter Bonds is when the government prints some bonds and drops them out of a helicopter, so whoever picks up the bonds now owns them. It's identical to a bond-financed lump-sum transfer payment. It's identical to a bond-financed lump-sum tax cut (because only net taxes=taxes-transfers matter). The government borrows money from the population by selling bonds, then gives them the money back, and lets them keep the bonds. At the end of the day the population has the same amount of money, and more government bonds.
If Ricardian Equivalence were true, Helicopter Bonds would have no effect on anything. It is exactly as if, when the government gives me a government bond worth $100, the government demands I give it my personal IOU (my personal bond) for $100 worth of future taxes. It is exactly as if the government and I simply swapped a government bond for my personal bond. And in the world of Ricardian Equivalence, where it doesn't matter whose name is on the bond, the net effect is zero.
Now let's consider a simple case where Ricardian Equivalence is false. Half the population is borrowing-constrained. They can't borrow. That means they want to sell their personal bonds (IOUs) but nobody will buy them. So Helicopter Bonds causes half the population to sell their government bonds to the other half, so they can spend the proceeds. Again, it is exactly as if the government and I swapped a government bond for my personal bond. But in this case, where Ricardian Equivalence is false, it does matter whose name is on the bond. Because only the government will buy a bond with my name on it, if I am one of the borrowing-constrained half of the population.
Quantitative Easing is the silly new name for Open Market Operations. It's when the central bank prints money to buy a bond. It expands both sides of the central bank's balance sheet. Qualitative Easing is when the central bank changes the composition of the asset side of its balance sheet, leaving the liability side unchanged. It sells government bonds, and buys some riskier or less liquid asset.
If we consolidate the balance sheets of the central bank and the government that owns that central bank, that means we can see Helicopter Bonds as a form of Qualitative Easing. The government/central bank swaps safe and liquid government bonds for less safe and less liquid private bonds. In my example above, where half the population is borrowing-constrained and unable to sell their personal bonds at all, Helicopter Bonds is just an extreme case of Qualitative Easing where their personal bonds are extremely unsafe or illiquid. In a less extreme case, the borrowing-constrained can borrow, but only from loan sharks.