Canadian here. Detergent is what you put in an automated dishwashing appliance. Dish soap could be either detergent or dish soap for washing things by hand. Dish pods are pre-bundled detergent with liquid that helps stains from forming.
Sometimes you see "dishwasher soap" or "dishwasher detergent" for the stuff you put in the machine, as opposed to "dish soap" which is used in the sink.
