Terminology for megatrees will tend to interact with terminology for other displays, rather than acting in isolation. The first distinction there could be: single color, multicolor, dumb RGB, pixel RGB. All of these can also be used on mtrees.
single color - obvious
multicolor - multiple distinct colors which do not fully blend (ie: red + green looks like red and green lights).
Could be Red,Green,Blue but could be other combinations of 2 - 4 or more colors.
RGB - color blending, red/green/blue effectively in same diffusers
dumb RGB - all of the lights in the same string show the same color (color is set by external controller)
pixel RGB (eg: SmartStrings or CCR): Each RGB light independently controlled by chip embedded in string
(It would be possible to have things like single color pixels, but nobody seems to bother)
Note that pixel RGB sometimes is done with in "pixel strings", sometimes in "pixel strips", and sometimes in "pixel modules" - in terms that Ray Wu would use. (dumb RGB is available in the same formats). Pixel strings have some wire between each cylindrical RGB LED/pcb/chip/sealant unit. Pixel strips are on flexible circuit boards enclosed in sealant. Modules are hard rectangular, square, or round chunks with usually multiple LEDs inside, separated by wires. We probably won't be able to change that industry usage.
All of this is background for various displays, not just mtrees. Mtrees (mega/midi/etc) only add the element of what you call strands and I think "segment"
There is also a term "multistrand" which has been around for a while, for when you twist multiple independent strands together; this goes back to incans; you might twist a strand or string of red lights with a separately controllable strand of green lights before using that multistrand in a megatree or other display.