And while the derivation for the decanter tray is quite logical, the "coasters" for individual drinking glasses do not move.
A seafarer can coast on a vessel and landlubbers can coast on a sled or tobaggan. While it is absolutely true, wwh, that "individual drinking glasses do not move", the coaster beneath the drinking vessel can be made to slide (or coast) over the surface of the table, much like a sled or toboggan, simply by pressing down on the drinking vessel and pushing in any direction. This is a common characteristic of any coaster, whether at sea, or propelled around a dining room on wheels, or pushed forward on a table to beckon a server to replenish the contents of the vessel. In each case, the coaster separates its cargo from the surface below and, in each case, it is the coaster which does the moving, not its cargo.