You question is kind of confusing, because you're mixing terms.
Hidden and direct and synonymous. Both are used in describing movement to a perfect interval by similar motion when the first interval is different that the second. Like a sixth to an octave with both voices ascending.
Parallel is more specific within the class of similar motion. Both intervals will be of the same type. Ex. a perfect octave to a perfect octave. "Hidden parallel octaves" is mixing terms. It's either hidden octaves or parallel octaves.
What if both voices move by contiguous movement?
If you move to an octave, and both voices move in contiguous (step-wise) similar motion, then by definition the previous interval must be an octave and the motion is parallel octaves.
What if one of the voices does not move?
By definition this is oblique motion. It's not similar motion therefore there can't be direct or parallel anything.
A few important concepts that you probably want to consider - if you haven't heard them already - are...
- Independence of lines. Parallel perfect intervals are avoided at least in part because the consecutive intervals are exactly the same. Such lines are merely a transposition. Lines in similar - or parallel imperfect intervals - are not literal transpositions. There a slight changes in the exact linear contour of the part and that provides some basic level of independence.
- Emphasize interval variety. In Fux the rule of thumb limit was 3 times for any consecutive interval. So even parallel thirds and sixth have a "limit." This is sort of a specific statement about linear independence. In effect it means you need to put in some contrary and oblique motion for variety's sake.
- Third and sixth help define the modal aspects of a key. Perfect fifths and octaves help define the important tonal degrees. In practical terms third and sixth are better in the interior of phrases and perfect fifth and octave for cadences.
- Relative motion "rules" are of special concern with the outer voices, the bass and soprano. When one of the voices is an inner voice, tenor or alto, there is less sensitivity about relative motion.
Some times it's good to keep positive ideas like those in mind. Those are the things you strive to do instead of worrying about prohibitions.