The 6 speed has no clutch plates, just discs, not using parts is cheaper to build. That is why you can only use Dexron VI fluid.
I was thinking of the two words as being the same. That is the clutch plate for a manual is actually a disc but instead of contacting another it contacts the pressure plate, a disc as well.
Each clutch should have a clutch pack, a series of discs where every-other-one splines to either the central shaft or the clutch drum or housing. The shaft is usually a series of concentric shafts, one around another. And the shafts provide the fluid flow for engagement from the valving.
I did find that this new design is unique in that it is easily adapable to other power ranges by simply adding more clutch plates, and probably by removing spacers.
page 6 shows the engagement pattern.
It does not show the ratio/multiplier engaged with each.
I also learned that the valving is partially done with PWM, pulse width modulation, to effect the rate of apply pressure, IAW parameters.
As to slipping into third gear when cold, I still don't have enough info. I do now know the clutch changes going from 2 to 3. There is a primary clutch used for 1,2,3,&4. It might be that is the only clutch for gear 1, but I have not yet figured out the other two columns which might be tied to reverse and engine braking.
For gear 2 another clutch engages. For gear 3, that clutch disengages and a different one engages. That clutch is also used for gear 5, so I need to get up to those speeds before it quits the funky gear 3 shift. That might at least eliminate the clutch itself, but not the release circuitry of two and how it effects 3 apply.
I've posted several places and no longer remember if I mentioned that in the TSB's a TCM problem was tied to the missing diode problem on the cooling fans.