Without any further comparison: Obama describes several similar incidents in his book where he didn't sign off on anything specific. Some of these drone strikes and also ground strikes (there was one in North Korea, actually - and this is one of the things Trump criticized Obama over, over having been.. at least according to "sources"... ready to pre-emptively strike North Korea over the nuclear weapons.. which ironically likely was the reason they have one to begin with) ... these strikes that no one really signed off on were then later pulled up to fairly obviously raise a political point about how the sitting president wasn't any better than previous ones, etc.

Obama never makes that point in his book, but given that what he says in it is roughly correct, the setup here with Trump is identical.