Mmmmm I don’t think you would say that two cars going opposite directions on a road , in opposite lanes, are on a parallel path, you would say they were on an opposite path, I would think.

But if those two cars were traveling the same direction, in the same two lanes, they would be properly described as following a parallel path.

from a line vs ray perspective parallel and opposite are equivalent, but when they are rays and not lines, directionality matters.