What’s the difference between the stuff that gets sprayed on crops and the stuff we buy in cans to kill insects at home?
Everything and nothing.
Insecticides work in various ways to disrupt the biology on insects, causing them to die. Some of those insecticides will (in sufficient doses) be quite effective in killing humans, as well. Others may only build up to cause long-term neurological damage or increased risk of cancer.
The reason that we have many different insecticides is that different chemicals are more or less successful in killing specific insects. Some insecticides will do a great job of killing insects, but will also destroy different varieties of plants. (So we might develop insecticide Aa to use against bug Ba, but we find that Aa will kill roses and peas, although it does not harm corn/maize and beans. If Ba eats roses, peas, corn, and beans, we can use Aa on the corn and beans, but we need to develop a different toxin to protect roses and peas. In addition, some insects are chewers and some are suckers, so while an insecticide that covers the surface of a plant will kill chewers, we may need to develop a special insecticide to get inside a plant to kill the suckers. (And once we’ve put the insecticide inside the plant, we have now made it more dangerous for people to eat, since it cannot be simply washed off and we need to worry about the accumulation over years.)
An example of all these issues can be found with the insecticide carbaryl. While there are opponents of its use (as with most chemicals), it has been employed for 45 years and is considered generally safe. If you go to your garden store, you will find Sevin® (a brand name for carbaryl) offered as a general purpose bug killer for your roses and peas. It is also used extensively by farmers, so there is no apparent difference, in many cases, between what you use in your garden and what you eat on your commercially sold vegetables. This is true whether it is sprayed on in liquid form or dusted on as a powder. You will note, if you pick up a package and read the directions, that there is a specific amount of time indicated between the last occasion when you may apply it to the plant and when you may harvest the plant. The manufacturers know that there should be some time for it to lose its effectiveness to keep from poisoning people.
On the other hand, carbaryl is also used in various systemic pesticides (meaning it is put into a solution that the plant will absorb so that it can kill sucking insects). Applied this way, there is a substantially longer period required between the last application and harvest. (Away from the rain and sunshine, protected by the plant, the toxin will survive longer.) If the sucking bugs are liable to come back and attack the plants before harvest, Ortho or Ciba-Geigy or Science will send their scientists out to develop a different bug killer that will break down faster inside the plant, so that it can be applied closer to harvest (although it will probably need to be applied more often, raising the costs). If the application of such specialty insecticides are deemed too dangerous to put in the hands of Joe Homeowner (who may misuse them) but it is felt that professional farmers may pay more attention to the directions, then the farmers’ insecticide will differ from the homeowners’. Once the chemical company thinks that they have a formula that will not cause too many deaths among the suburbanites, they will re-package it and sell it in quart jars instead of fifty-gallon drums.
Generally, the products we “buy in cans” are not intended for use on plants. They are either used as general fly and mosquito killers or to kill wasps in their nests or ants, roaches, and other house (not garden) pests. As such, they may have quite different compositions. Frequently, in these cases, they use pyrethrins that kill quickly on contact, then break down quickly to avoid residue build-up. Because they break down so quickly, they are rather unsuitable for use on plants, since you would need to apply them once a day or more often. Some of the garden chemicals are also sold in cans for house use, but not often, because of the different ways in which they need to be used.
So, we do use the same products in the home, garden, and farm on some occasions, and we do not in others.