"Pluck" has the sense of pulling something. You pluck feathers; pluck at someone's sleeve; but you pick up sticks.
We talk about "picking" fruit in general (and picking flowers or potatoes) even though in some cases you have to "pluck" the individual fruit from the bush!
![Embarrassed](https://cdn2.able2know.org/images/v5/emoticons/icon_redface.gif)
Maybe because in that case you don't have to pull very hard, when the fruit is ripe.