Right. I know that they are chemically different, though similar. If you try to get through grease with a soap you're going to need an acid rinse agent to remove the soap residue. Hence my vinegar as fabric softener trick.

That's also what caused decades of soap rings on bathtubs, something we haven't seen in our lifetimes as many commercially available bar soaps and bubble baths became formulated as detergents. Personally I now find, on a gut level, white bar soap to be scarily white and excessively perfumed. I prefer a handmade soap that really is a soap, and as such I'm learning to clean more like the way my great-grandmother may have done.