Yes, these are different and separate exchanges that were originally separate from the New York Stock exchange (now all are owned by the Intercontinental Exchange group).
Most of them are electronic, meaning that trades are completed electronically through the computers in the exchange's data centers (in Mahwah, NJ) rather than on a physical trading floor.
From the regulator's point-of-view they are still treated as separate exchange with separate members, separate listings (though most stocks have one exchange that is the 'primary' listing, and other 'secondary' listings), separate rule-books, and different fee-schedules. Many members are members of more than one exchange, and most of the rules and pricing are similar. Most of the exchange servers now run on much of the same software as the other exchanges, with slight variations to account for the differences in rules.
One way to look at the relative importance of each is to see how much volume is trading on the exchange you are interested in. BATS (now owned by CBOE) offers a real-time report: