IFR C172 departure from OSU reportedly received confused ATC instructions from CMH Departure; which prompted a course correction from the Departure Controller.

Narrative

Filed OSU direct APE V144 LDN ZZZ; and was cleared as filed. This flight plan was loaded in panel-mounted IFR GPS unit. OSU ATC issued right turn to 050 vector with takeoff clearance; Runway 27L. In turn to 050; was switched to CMH Departure in the climb and after established on the 050 was advised to 'proceed on course.' I acknowledged the clearance and turned southeast to re-intercept the previously cleared course (direct routing between OSU and APE). As I intercepted the course line and began a turn back to the east-northeast direct APE; the controller queried my heading and asked if I needed assistance with a vector to APE. I advised my present heading and that I was proceeding direct to APE (as previously cleared). If the controller wanted me to fly direct to APE from present position; the appropriate clearance would have been 'cleared direct Appleton' or 'proceed direct Appleton' not 'cleared on course'. There was no other traffic in vicinity so there wasn't any hazard involved; but a potential exists for misunderstanding of the controller doesn't specify present position direct if that is what is intended.