Sizes:
The three different sizes are most commonly referred to as:
LARGE
MEDIUM
SMALL
Groupings:
TRIO: Any grouping of three pieces, one of each size, is called a Trio. When listing components, a Trio of a given color is understood to be a monochrome trio.
TREE: When a Trio is stacked in the arrangement that makes it look like a little pine tree, it's called a Tree.
NEST: When a Trio is nested together with the Small inside the Medium inside the Large, it's called a Nest.
It's not uncommon to drop the extra syllable and say Tree when you mean Trio, especially since it's frequently ideal to stack Trios up as Trees.
For example, in Volcano, Trees are not needed particularly, but the scored pyramids are usually stacked as Trees to make them easier to view. This is just for convenience, and your scored pieces may be rearranged at any time.
Colors:
The pyramids come in ten standard colors: Red, Yellow, Orange, Green, Cyan, Blue, Purple, Clear, Black, and White.
MONOCHROME TRIO: A Trio with pieces that are all the same color
MIXED-COLOR TRIO: A Trio of pieces that are not all the same color. (They could be all different, or two of one color, and one of a different color.)