3 axis rapid interpolation does not, IMO, determine whether a machine is a true 3 axis machine. On some machines, you can turn this option on or off in parameters, so that certainly does not mean you have changed the capability of the machine.
Machines that move at maximum rapid speeds will drive the machine in a series of straight/45 degree angles, as the axis with the longest distance to travel will move by itself until it reaches a position where the remaining movement is the same as one or more other axis, at which time both axis will move together (the 45 degree move). 3 axis interpolated rapids do give a programmer a better concept of where the tool moves, whereas the 'max rapid' concept, with its attendant dogleg moves, can sometimes surprise you, even in 2 axis mode, as you drill bolt circles in cramped quarters, where clamps can unexpectedly get hit during a dogleg rapid move.
3 axis linear interpolation is the definition of a 3 axis machine, IMO. Way back in the beginning of cnc, some controls could not do this, but I don't think this is a major concern with most controls made within the last 10 or 15 years.
I have never heard of a machine yet that could cut arcs in any but one of the three standard planes at a time (unless it is a 5 axis machine), but the majority of 3 axis CAM software generates gcode that attempts to simulate 3d curves by means of short segment linear movement. This software commands a higher price, "just because" its not as simplistic as top down 2 axis paths.