The difference between trader and broker is the same as the difference between player and referee.
A trader is one who trades in the market and makes/looses money.
He is the one who buys/sell shares.
A broker is one who provides platform to a trader to trade and make money,
a broker makes money per trade executed by a trader.
Trader earns/looses money based on his skills whereas broker earns on every trade a trader executes irrespective of his gains/loss.
Its just like, player gets rewards based on his wins/looses in matches, whereas referee gets paid for every match irrespective of loss or wins by players.