Commercial pre-mixed neem oil sprays often contain a refined neem oil extract.
The real deal, pure neem oil, is colored, cloudy, and very smelly (a kind of sulfurous, nutty, garlic smell).
Commercial neem oil sprays often contain a refined neem oil extract. Neem oil extract has a lower 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 (product link), 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.
When you purchase neem oil read the label. Not all neem oils are made equal. Some products for sale are actually neem oil extracts. They do not have a high concentration of the insecticidal ingredient Azadirachtin. Look for 100% pure neem oil, also called raw or crude neem oil.
Make sure it's cold pressed and preferably organic neem oil (product link). Heat destroys Azadirachtin. Buying organic neem oil ensures that it is not contaminated with solvents or petrochemicals that may have been used in the purification process.
Store your neem oil in the refrigerator, or at least as cool and dark as possible, and it will keep longer. It should keep for a year or two.
Neem oil can solidify at low temperatures. If it has gone lumpy you need to warm it up by placing the container in warm water. Warm, not hot! 85F (30°C) is plenty. Remember, heat destroys Azadirachtin, and Azadirachtin is what affects the insects.
Neem oil does not mix with water. You have to add an emulsifier. (An emulsifier is any substance that makes oil and water mix, e.g. soap, detergent, shampoo.)
Use insecticidal soap. You could in theory use any liquid soap for this, but it's safest to use proper insecticidal soap. Insecticidal soap is a highly refined liquid soap that will not hurt plants. Household soap may burn or otherwise harm sensitive plants.
Learn more about making, using and buying neem spray: