I find the word parallel to be more helpful to those studying harmony. It is the parallel motion of voices with certain intervals that is discouraged.
If for example you had Soprano / Alto:
C/G, D/G, C/G
There is oblique motion of the intervals, not parallel motion. So this would be fine. The beat in which these intervals fall is unimportant, what we are concerned about is motion between different sets of intervals. C/G may repeat at a different point in the music, but again, the movement between intervals in this example is not parallel.
Next example:
F/C, F#/C, G/B
Here we have two fourths that have the same numerical distance, but different quality. This is OK. The movement between intervals 1 and 2 is oblique, and between 2 and 3 contrary. Intervals considered to be in parallel motion must be of the same distance and quality.