Understanding the difference between quantitative easing and helicopter money

Quantitative easing and helicopter money are often contrasted in the following manner: it is claimed that quantitative easing consists in giving money to financial intermediaries (who do not need it) while helicopter money consists in giving money to households that need it. In reality, we have to be much more precise: Pure quantitative easing is a purchase of bonds (especially government bonds) by the central bank, which pays by creating money. The sellers of these bonds therefore hold fewer bonds and more money; If quantitative easing is combined with an increase in the fiscal deficit, we end up with a transfer of money by the central bank to the beneficiaries of the fiscal deficit (increase in public spending, increase in public transfer payments or tax cuts); There is therefore an equivalence between the combination quantitative easing + increase in the fiscal deficit and helicopter money under two conditions: The beneficiaries from the increase in the fiscal deficit are those targeted by helicopter money; Quantitative easing is irreversible (there is no resale of the bonds purchased by the central bank, which are rolled over at maturity).