There are two participants that you see on a 'listed' level II, ECN's and Specialists.
Specialists are employed by member firms of the exchange. The are not paid by the companies they make a market for. In return for creating a liquid market and taking on huge amounts of risk, they are allowed special trading privaledges, such as trading ahead of order flow (information flow) and naked shorting. Most Specialists cover several stocks unless they are making a market for a very active stock like IBM etc, in which case they most likely dont have to time to do it. There are only a few open outcry exchanges left where people actually bid and offer stock in person. NYSE, AMEX I think are the only equity outcry exchanges left. PACX (pacific exchange) is electronic as is MDWS (midwest). CBOE is the Chicago Board of Options Exchange. They trade equities there as well, not sure if they have gone all electronic yet.
ECN's are represented by the NASD and NASDAQ symbols. They can represent both retail and insitutional electronic order flow.
Just an fyi as well, Market Makers are found in OTCBB and Nasdaq stocks, they are not involved in 'listed' NYSE and AMEX stocks. They work for broker/dealers and buy and sell for their own accounts as well as execute orders for customers. If and when a broker/dealer wants to make a trade they either call down to the Specialist or put the order themselves using an ECN(which are anonymos).
Sorry for being long-winded, hope that answers your question.