I also have no experience with dishwashers, so how different is dishwater detergent from regular dishwashing soap?
I use a brand of dishwasher tabs that are supposed to be more “natural” and never use rinse aid, to no ill effect. Personally I think the normal tablets and rinse aid are specifically designed to be used together.
It also seems to be the water used about 4 liters of water in commercial dishwashers vs 12 liters for household types. Commercial use less water, more powerful detergent, no water rinse.
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.