Language is use .. which is probably why Wikipedia and vigilance serve as a better dictionary these days than Oxford.
I think your first item is more accurate as systems should really be looked at as:
General Purpose/{Single, Limited} Purpose
As we've got devices going both ways .. Like i used to say of cameras, the most useful computing devices are the ones you have on you - so as I see it - you've got much of the small mobile market attempting to become General Purpose these days, and in the high end space - we've really got the reverse in many places as ppl are attempting to do more single/limited things closer to the hardware with general purpose servers and workstations.