What I find especially odd is that the 'C' is so often put after the width in millimeters. The wheel size designation is '700C' (which is not, in any practical sense, a real measurement of anything). Following the width in millimeters with half the tire size designation is confounding for new riders. I understand =why= it's done, I just don't think it's a good idea.
It would be so nice if we could just dump the meaningless and obsolete designations in favor of bead seat diameters and metric widths. Of course, if we eliminated the confusion then everybody would be able to order their own tires with confidence instead of throwing up their hands in disgust and paying the LBS premium to figure it out.
In any case, I always refer to tires either by BSD and width or, if necessary, by the French size and metric width. So I would call your tire 700C x 35mm or 622 x 35. According to Sun the rim is specified as 622mm BSD, 612mm ERD , 22.5mm width and 15.5mm depth.