1. When you make a lather, whether it be to shave your face or put detergent in to washing machine, that lather is not soap, or detergent.
The lather is, in fact, millions of tiny bubble -- in other words, pockets of air tied up with a film of water.
2. When you use soap or detergent, neither is the "cleaner." Water is the "cleaner," in every each case.
Soap or detergent is used primarily as a wetting agent. It changes surface tension of the water and allows it to come in close contact with the dirt. (Dirt, whether it be greasy or not, tends to repel water normally.)
You can check this action out by taking a whole, unbroken, ripe tomato. Run a little cold water over the tomato. The water runs off immediately, leaving only a few rounded drops of water on the surface.
Now, wipe your finger over the tip of the dish washing liquid cap...just a smidgin of detergent on your finger....and now wipe this detergent over the tomato. Repeat with the same amount of water....you will find the tomato is "wetted." A similar trial can be done with your feet...before washing them, that is.
The important lesson from this: Using more detergent or soap than really necessary, does NOT improve the cleaning of your dishes. Only just the right amount, a very tiny amount in fact, is needed... no more.