The first three are probably the same, though you would have to read the labels on any product to make certain. Insecticidal soap is usually composed of a potassium fatty acid to form a true soap designed to be very effective in breaking down the protective coating on soft bodied arthropods.

These soaps are a contact killer and must be applied directly to the pest or where the pest is likely to some into contact with the liquid while it is still wet. Once dry, insecticidal soaps don't do anything to anything.

Neem oil is a plant derived product with many different kinds of uses. I strongly suggest that you simply use the Google search engine to do your own research....perhaps using NEEM OIL INSECTICIDE as your search words. Then, if you still have questions after doing a little bit of reading, please come on back here.

I always keep insecticidal soap AND neem oil on hand and find many uses for both of them.

Neem Oil is derived from the sees and fruits of the "Azadirachta indica" tree that is native to parts of India. Various parts of this tree have been used by the native population for centuries for many things, and then the potential sales in the richer parts of the world was discovered, some way for someone to make a profit.
Neem Oil products can be of use, but other methods of pest and disease control would be better then relying on even this much because many of the other products have been so overused that the insects and disease are starting to show resistance to them.
Rhizo described Insecticidal Soaps quite well.

Thanks rhizo, I have always respected your advise. I too have both soap and NEEM and have used them according to others recommendations, so I guess the bottom line question I have is which is safer? I love my Praying Mantis! I have learned to hand pick the bag worm sacs in the fall/winter, and despise using the kill-all products in the spring to get the emerging larvae. So what can I use to get these beasties? My reading suggests that NEEM will last longer, and BT won't ... so, how can I get them under control without hurting my Mantis? Thank you.