From a mathematical point of view: no, no directionism at all.
From a physicist working with spins point of view: yes, parallel has the same direction and antiparallel the oposite.
Each area create their own jargon. Sometimes it's confusing to ousiders and when you pick a book from another area you must double check that the worlds mean what you think their mean.
For what it's worth, protein structural biochemistry uses similar terminology for sheets. Since a strand has a direction (N to C), sheets are 'parallel' when neighbouring strands are pointing (roughly) in the same direction, and 'antiparallel' when pointing in opposite directions.
