Where most beginners of the art of CCPM stumble is when they confuse the terms aileron, elevator, and pitch CHANNELS with the terms aileron, elevator, and pitch FUNCTIONS.

Once you seperate FUNCTIONS from CHANNELS ... you'll get a better "feel" for the CCPM big picture.

FUNCTIONs are what the swash needs to do to make the heli fly: ie Pitch FUNCTION moves the swash up and down (for most helis) on the main shaft, the aileron FUNCTION tilts the swash left/right and the elevator FUNCTION tilts the swash fore and aft.

CHANNELS designate which RX slot the servos are plugged into. IE: Futaba designates ch1 as aileron, ch2 as elevator, and ch6 as pitch.

In order to determine the swash config for your heli ... you need to know which channel(s) are needed to perform each function.

With the NORMAL swash config (ala TT Raptor) ... the aileron channel is the only channel needed to cause an aileron function (doesn't need any other channels) therefore no "mixing" is required in the TX (at least not for those functions).
Elevator FUNCTION requires only the elevator CHANNEL
Pitch FUNCTION requires only the pitch CHANNEL

In this config, the TX setup is fairly easy however all the extra levers and linkages add weight to the heli. For 30 size helis and up, the extra weight is not a big factor but for the smaller electrics where weight (or lack of it) is very important ... the less mechanical stuff on the heli the better.

Enter electronic CCPM ... stage left.

As you said, the 120° swash config is probably the most commonly used swash config ... especially for smaller helis ... but does require TX channel / function mixing (electronic CCPM) because all the mechanical stuff has been removed to save weight and reduce the servo-lever-swash link complexity.

Again ... you need to know which channel(s) are needed to perform each function. When you map the servo/channel(s) needed for each function in this swash config, you'll see the difference compared to the normal/non-ccpm config.
Reference the 120° config again:


For the PITCH function to work, you need help from all three servos (normal swash only needs the pitch channel). You need ALL three channels to work together to raise and lower the swash.
The aileron function needs two servo channels (normal swash only needed the aileron channel) which are the aileron channel and the pitch channel.
The elevator channel needs ALL three servos (normal swash only needs the elevator channel) which are pitch and aileron servos moving half the swash in one direction and the elevator servo moving opposite to the other two.

This in itself requires some mixing of channels but this only describes one input at a time.

Now imagine changing your pitch (moving the collective stick) while inputting both aileron and elevator stick movements. Take the aileron servo/channel for example. It's commanded position is based on a MIX of ALL three swash functions (aileron, elevator, and pitch). The pitch servo/channel commanded position is based on a MIX of ALL three swash FUNCTION also.
The elevator servo/channel commanded position is based on a MIX of elevator and pitch FUNCTIONS
This is the heart of CCPM (electronic CCPM).

The end result is for a NORMAL swash config heli (ala TT RAPTOR) is slightly more complex mechanical setup and possibly heavier but less difficult for TX setup where as the CCPM configs offer a lighter and less complex mechanical setup but requires a TX to support the specific swash config and slightly more challenging to setup in the TX. Of course, once you get your head around programming the TX ... it'll become second nature and will "seem" just as easy to program as the Normal config TX setup.