An A's an A's an A: Not so.

Guitar players I think tend to work in chord positions and what will provide good-sounding back-up for songs. Pianists who also play a harmonic instrument seem to work in inversions. The difficulty occurs because guitars generally have six strings, and thus six notes available for each chord. The piano has ten notes available. Think of the differences in sound between the B7 done on the first and second frets and the 'same' chord done in the A position on the 2, 4 and 5 frets. They are the same chord but they don't sound the same. Maybe some of what you're calling parallelism is attributable to that sort of thing.