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The Deluxe Joystick differed from the original in a number of ways. All joysticks sold by Tandy for the CoCo were analog joysticks, but the Deluxe Joystick had two 'fire' buttons -- a red one and a black one. The red one was button one, and corresponded to the button on the original joystick. Button two could only be used with a CoCo 3, as earlier Color Computers lacked the hardware to test it.
In addition to the second button, the base of the joystick is larger. More significantly, the Deluxe joystick included hardware that could automatically center the stick on the X axis, the Y axis, or both. By holding the stick to the lower-right corner, flipping the unit over, and latching or unlatching two spring-loaded clamps internal to the stick, one could select which axes were self-centering and which were free-floating like the original joystick.
This feature allows the user to select the best stick configuration for whatever program they're using. For maze-type and platform games, gameplay is often enhanced with self-centering joysticks that more closely mimic a digital stick. For paint programs and games like Polaris where you are moving a cursor around on the screen, a free-floating stick is preferable. And for flight simulators, it is nice to have a throttle control that is centered in the X axis, free in the Y axis, and a control stick that is centered in both.
Though generally more robust than the original CoCo joystick, the centering mechanism in these joysticks is somewhat fragile and can break or come apart.
The design of the stick seems to be nearly identical to a stick marketed for the Apple II by Kraft, so it was probably licensed by Tandy. A joystick of the same design was also branded by IBM for use on the PCJr.