[SAI_Peregrinus]

Rinse aid is a detergent that helps remove the residue other detergents or minerals in the water might leave on dishes after washing. It's not needed for hand washing, where mechanical scrubbing & a rinse with clean water performs the same task.

Dishwasher detergent is a surfactant, but is not a soap. All soaps are detergents, not all detergents are soaps. Soaps form insoluble precipitates when used with "hard" water, dishwasher detergents don't do that. They're not good to touch directly (rather harsh on the skin, they'll remove all the oil) but since they don't form those precipitates they work in a wider variety of conditions than soaps do. They also tend to include some other components, like bleach. That helps them clean better without needing mechanical scrubbing, which dishwashers don't do.