The clarified hydrophobic extract from Home Depot doesn't pack the full punch.
Cold pressed neem has a mix of azadirachtin and other triterpenoids-limonoids (the class of molecules), each with varying degrees of insecticidal activity. This table summarizes the effects well.
Screenshot_20180512-160640-01.jpeg
Table from this publication, a solid read:
http://www.scielo.br/scielo.php?scri...92000000400001
And this one too:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5061770/