NASDAQ (where AAPL and MSFT are primarily listed) usually have multiple market makers in each stock. If you have level 3 quotations you can often see which market maker is posting the quotes.
NYSE have a specialist (now called Designated Market Maker) on the floor, who resides in the booth. Each booth has a number of stocks assigned to it.
There is not usually a strong relationship between the company (e.g. AAPL) and the market maker, rather the market maker is simply a type of proprietary trader who wants to make markets in that security, and has figured out how he can make money doing so, so much so that he is willing to commit himself to providing continuous quotations to buy and sell that stock.
Most exchanges require at least one market maker for a given stock, particularly if the company is primarily listed on that exchange. The number of market makers depends on the exchange rules, and how much liquidity each market maker provides.