Organic food is food grown in a church organ. Organised crime is crime committed by organists.
Well, etymologically speaking.
Once upon a time, the ancient Greeks had the word organon which meant something you work with. An organon could be a tool, an implement, a musical instrument or a part of the body.
Originally, an organ was any musical instrument, but in the ninth century people decided that every church should have a pipe organ in it for, as Dryden put it, "What human voice can reach the sacred organ's praise?"
Slowly the pipe part got dropped and other instruments ceased to be organs (except the mouth organ, which, if you think about it, sounds a bit rude).
Organ continued to mean part of the body, hence the old joke:
Why did Bach have twenty children?
Because he had no stops on his organ.
Anyway, the body is beautifully and efficiently arranged (at least my body is). Each organ has a particular function. I have a hand to hold a glass, a mouth to drink with, a belly to fill, a liver to deal with the poison and so on and so forth. Heart, head, lungs, liver, kidney and colon each performs a particular task; and the result, dear reader, is the glory that is I.
So if you arrange a group of people and give each one a particular job, you are making them act together like the organs of a body. You are organising them.
Thus an organisation: something in which each person, like each organ of the body, has a particular task. And though that shift happened in the sixteenth century when everybody liked metaphors about the body politic, crime didn't get organised until 1929 in Chicago, which shows how lackadaisical most malefactors are.
A bunch of organs put together make up an organism, and things that are produced by organisms are therefore organic. In the twentieth century, when artificial fertilisers were strewn upon our not-green-enough fields, we started to refer to organic farming and thus organic food.
However, the church organ survives. If you add pipes to an instrument, you are organising it; and organ music can still be referred to as organic.
A reluctant organ donor