If one is playing (double stops) in thirds in C (i.e., playing the scale of C in thirds) one plays the scale of C (C, D, E, F, G, A, B, C) simultaneous with (E, F, G, A, B, C, D, E). In other words: CE, DF, EG, FA, GB, AC, BD, CE.
To figure out what to play, one consults the key of C, notices that E is the third in that scale, and so on...
Why is the third associated with the rest of the notes in that scale not the third relative to each of those notes (i.e., DF#, EG#, FA…)? What is the rationale behind saying: playing 'DF, EG, etc.' is playing in thirds?
(This may appear a silly question for a piano player for whom each finger position is different. But for a guitar player, the question seems more reasonable. Also, it seems absurd when you extend it to all scales and realize all the thirds you'd be playing are the same, regardless of scale. However, it's very relevant if you're trying to figure out how to accompany a melody, note-by-note in thirds [Is it signature-same throughout the piece, regardless of chord change?].)