Dave, where is that thread from long ago, where I defined the US/Canadian terminology?
Perfect tiling, "thinset" has come to be the generic word that it used for a cement-based setting material that is used to set tile or stone, or to install mats and membranes. By its name "thin", it is meant to be installed in a "thin" layer, and is almost always used as an adhesive only. The only thing that I would correct Dave on is the use of "thick bed". Thick bed in North America is what you call a "screed". Thick bed materials are rarely used to set tile directly, but when they are, a bond coat or "neat coat" is used to bond the tile to the still-workable screed (we say mud bed).
We do have products that are in between "thin" and "thick", and used for setting tile and stone, which we call "medium bed mortars". These have larger sand and other additives that reduce or elimnate shrinkage, and thus can be built up to ~3/4" under individual tiles.