A trader represents the entity which owns the power while the trading process is taking place. For example, the trader may buy power from a producer and sell it to a retailer, or the trader may choose to buy power from one retailer and sell it to another retailer. There are many routes from the producer to the end-user.
Brokers play the same role in the power market as estate agents do in the property market. A broker does not own power, but instead acts as an intermediary. A retailer may, for example, ask the broker to find a producer who will sell a given amount of power at a given time.