Dishwasher detergent is more likely to contain phosphates and surfactants than laundry detergents. Unlike in laundry machines, there is no agitation in dishwashers. Dishwashers work by spraying water containing detergents with chemicals that will dissolve and break down the food residue stuck to the dishes. If these chemicals somehow make it through your septic tank without killing the bacteria, they can eventually enter the soil around your tank, leaching into ground water and putting you at risk for contaminated drinking water.
Look for Phosphate Free dishwasher detergents.