Brokers

Brokers are intermediaries in the secondary market, that execute buy and sell orders for clients.
They charge commission.
When an order comes in from a client, the broker has a number of options:
1) match the order with other clients
2) trade themselves (if they have an account)
3) sell the order to a market marker
4) route the order to somewhere else

Dealers are intermediaries in the secondary market, that buy, sell or short securities for clients
They do not charge commission but just mark up the price

Market Makers have their own account and they control the bid-offer prices

Inter Dealer Brokers are intermediaries between the market markers
They do not have their own account and charge commission

Broker Dealers are brokers and dealers and have their own account

Brokers - A dealer who is long on dollars and anxious to sell may not wihc to reveal their position to others. The desire to sell say $50m for sterling at a given rate can be passed to a broker who will disseminate this information anonymously. Another dealer who finds this rate acceptable may close the deal via the broker. The broker takes no risk. The clients settle directly and the broker takes a small commission.