Answer: Commercial neem oil sprays contain a refined neem oil extract.
Neem oil extract has a very low concentration of Azadirachtin, and Azadirachtin is the ingredient that affects insects.
There are other ingredients in neem oil spray that show insecticidal properties, but Azadirachtin is responsible for 90% of the effect of neem oil insecticide.
The real deal, pure neem oil, is colored, cloudy, and very smelly (a kind of sulfurous, nutty, garlic smell). Commercial neem sprays smell better and are convenient, because ready to use. They just don't work anywhere near as well.
Making your own neem oil spray is simple, much more effective, and if you do a price comparison it's also cheaper in the long run.
There is of course a downside. During times of drought stress or high humidity any oil spray can injure plants. The more refined oils, like the neem oil extracts, are less likely to cause injury. However, even they are not totally safe to sensitive plants, and the not sensitive plants will be happy with your raw neem oil spray, too.
Neem oil is perfectly safe for humans and pets. I don't have recipes available but you can do a web search and find some, I'm sure.
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