True donations are not taxable in the UK, because they are not part of a trade.

In other words, they are not given in exchange for something; the something is freely given without the donation.

Of course there is the question of whether something is truly a donation. But charities have to deal with that question, so there are formulaic approaches to it, and advisors. Sometimes the wording that accompanies a donation must be written carefully, to clarify what is and is not expected for it, because donations can be directed to a purpose, which isn't (apparently) the same as paying for something.

I assume it's similar elsewhere?

"Tax-deductible donation" is a subset of "donations", at least in the US. I can "donate" (syn: "give") money to anyone. I don't have to do anything special for that, and in theory they should report it on their (personal) taxes as income. If I'm giving it to a registered charity (non-profit), I can deduct it as a donation on my taxes. Maybe that's part of why this piece generated so much discussion: for some, just the word "donation" carries certain connotations that others might not ascribe.