The acronyms HDE and CDE appear to be unique to Align. They refer to how the swashplate on the heli is controlled.
In an HDE system, each of the three swashplate axes are controlled by a single servo. One servo tilts the swash forward and backward, one servo tilts it left and right, a third servo moves the swashplate up and down to operate the collective pitch mechanism. the fore/aft and left/right inputs are at 90 degrees to each other.
In the CDE system, the swashplate movement is controlled by three servos acting in tandem. For fore/aft control, two servos move the rear of the swashplate up, while the third servo moves the front down. (and for the other direction, the same two servos move the rear down, while the third servo moves the front up). For left and right, two servos work in tandem to tilt the swashplate left and right. One moves up, the other moves down. The third servo does not move. To move the swashplate up and down for collective pitch control, all three servos move the same direction to move the swash up and down. In a CDE system, the inputs to the servo are generally 120 degrees apart, instead of 90 degrees. One ball on the swash is located along the nose - to - tail axis of the heli, the remaining two balls are 120 degrees away from this ball, one on each side of the heli (some helis place the swash balls at 140 degrees -- one in-line with the nose-to-tail axis, the remaining two balls 140 degrees from that ball, one on each side of the heli).
As to what the two terms actually stand for, I looked at the Align site and didn't find a good explanation. For what it's worth, Kyosho calls their equivalent of HDE "MMS" (for mechanical mixing system), and their equivalent of CDE "EMS" (for electronic mixing system).
Properly executed and set up, it is hard to tell the difference between the two systems in flight. In the smaller helis that are using micro servos, the CCPM (CDE) setup is most likely the better system to use, as the load presented by the swashplate on the small servos is shared by three servos, lessening the need for high torque servos.
Generically, the CDE setup has been referred to as "CCPM" (cyclic-collective pitch mixing) for about twenty years or so, and refers to a system where three servos are used in tandem to control the swash movement. Some have tried to be "more precise" and refer to this setup as eCCPM, the "e" standing for "electronic". They argue that all helis have cyclic-collective pitch mixing, and the "e" is needed to distinguish between the traditional method and the electronic method. Others claim that the CCPM setup refers only to helis that move the swashplate up and down for collective pitch (as opposed to the early Schluter machines that used a rod running in a slot in the MR shaft to operate the pitch mechanism). Historically, CCPM was coined to indicate that three servos work in tandem, mixed within the TX, to move the swashplate