Generally, a gantry robot is a sub class of Cartesian robot. But a Cartesian robot may not necessarily be a gantry robot.
Cartesian refers to the arrangement of mechanical drives (motors) exactly matching the X,Y, and Z coordinates. A Cartesian robot contrasts from what we normally think of a robot: that is, an arm with various joints. A Cartesian robot is more like the typical 3D printer arrangement but can be as large as a building sized gantry systems.
Yes, a typical 3D printer is a type of Cartesian robot. In the typical arrangement where the Y axis moves the entire bed fore and aft below the nozzle it would not be considered a gantry system. Some higher end 3D printers which leave the bed stationary could be considered a gantry system.
A gantry robot typically has the X and Y mechanical components located substantially above the work area. Leaving the work area mostly clear of any supporting structures and mechanisms.
Cartesian robots are relatively simple because the X axis commands only move the X axis motor, Y commands only move the Y axis motor, etc. Non-cartesian robots (jointed arm and delta) require a complex series of coordinated movements of several motors when just moving in the X, Y, or Z direction. This complex series of coordinated movements requires complex inverse kinematic algorithms to calculate the various motor movements.
