Boxwood is commonly used because it is easy to work with and has excellent carving characteristics and is most often used for the white chess pieces.
However since it stains real well other wooden chess pieces may have a different wood look but will actually be stained boxwood.
This wood is from the deciduous tree native to the Indian sub-continent, it usually grows around the rivers.
The color can vary depending on the species; it is known for its excellent polishing and finishing characteristics and is very tough to carve, so any detail in the chessmen is due to skilled craftsmen that did the carving.
The most often used heartwood of this tree is deep and slightly grained black, the grain can be irregular and usually it is straight. Like rosewood it is hard making it difficult to carve so a tip of the hat to the skilled craftsmen that do an excellent job.
Common wood used for chess boards, this heartwood may vary in color but it is usually features a grayish-brown background with irregular dark streaks. It has excellent staining and polishing characteristics.
Regardless what wood is used to design the chessmen or chess boards the bottom line if it is appealing to your taste then it is the right set for you.