While both brokers and traders can work with the sale of securities (like stocks and bonds), the main difference between a broker vs. trader is that many types of brokers exist in various industries. On the other hand, traders primarily work in finance, making securities sales and purchases for a financial institution.
A punter is a speculator who makes large bets on unlikely outcomes with the hopes of beating the odds for large payoffs. A punter will often place a trade on a whim or gut feeling, or with little to no research or due diligence. The term is mostly used in the U.K. and in Australia.