Sizes:

The three different sizes are most commonly referred to as

SMALL

MEDIUM

LARGE

Orientation:

UPRIGHT: A pyramid standing with it's point upwards is described "upright"

FLAT: A pyramid on it's side, with the point along the playing surface is described as "flat"

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.

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.)

In Color Wheel, we also use the term GRAYSCALE to refer to the collection of Clear, Black, and White pyramids which are used to track your turns, to distinguish them from the rest of the colors which are used to fill the board.