(anecdotal:) Most people all over the world think 'organic' when it's not about organic chemistry or a list of 'approved' things or a label some agency sticks on things that are considered 'organic'. Organic in the sense of organic pesticides are the kinds of pesticides that you'd find in the wild, without them being man-made. That doesn't exclude synthetic replication, because if you can mass-produce that thing that was already there anyway, that's a good way making it available for more uses. That said, some 'organic pesticides' may be introducing an insect that is a predator to the insect you are trying to get rid of. While a 'pest' in 'pesticide' doesn't mean just insects, you usually have organic predators that don't harm your produce while hunting the pest that does attack it.

Say you have a fungus that eats at your corn, maybe there is another one that just eats that fungus but leaves the corn alone. Or maybe you have some insect that eats your wheat, and some naturally occurring compound exists that is bad for the exoskeleton of that insect; put compound (found naturally or replicated synthetically) on the wheat, insects will be sad/dead/gone, there ya go, organic pesticide.

Those natural, or, organic pesticides usually evolved with some specific target in mind, while man-made pesticides are more like chemo therapy: kill as much as possible without killing the produce we want. This has the downside that killing as much as possible actually kills things we don't want killed.