In don't think there's any standard about it. Cartesian means the tool moves in xyz. The other has a fixed gantry. If it followed any standard it would be called Y/X table according to ISO/FDIS 841:2001(E).
OpenBuilds OX CNC Machine vs. OpenBuilds MiniMill But this is just the way I perceive it. Technically they both Cartesian but the minimill is the only one of the two that uses an X/Y table. As Joe indicates there is no real standard.