BT stands for Bacillus thuringiensis so it is a bacteria and not any bug juices. BT works by paralyzing caterpillars guts so they stop eating and die.
Now, bug juices purpose is to kill the bugs with their own viruses and/or bacterial diseases that they carry. Every living thing is carrying their own germs. This is completely different approach than BT. And yes, the bug juice AND BT were popularized by "Organic Gardening" a magazine published by Rodale. Barbara Oh my, That was an old Rodale publications hint for destroying garden pests: To rid an infestation of say, japanese beetles, collect a quantity by picking and blend them in water. Spray the suffering crop with a diluted solution. The underlying theory being, a pest carries its own parasites that can be used against it. Must be effective if they do it commercially. Chuck I ruined my hands in the ring ... the referee kept stepping on them."