When the PlayStation 2 computer entertainment system was announced, the DualShock 2 Analog Controller (SCPH-10010) included with it was almost exactly the same externally as the previous DualShock analog controller, except that it was black (other colors came later), had different screw positioning in the back which counted one fewer screws, and the DualShock 2 logo was added. Another way to tell the DualShock and the DualShock 2 controllers apart is that the connector that plugs into the console matches that console's memory card shape; the DualShock’s connector has rounded shoulders and DualShock 2’s is squared off. The analog sticks were also noticeably stiffer for more accurate movements. Internally, the DualShock 2 was lighter and all of the buttons (except for the Analog mode, start, select, L3 and R3 buttons) were readable as analog values (pressure sensitive).
Source: Wikipedia, "DualShock", available under the CC-BY-SA License.