In most cases the directional tells what way the street runs from the division line(s). But in others, it tells that the whole street/road itself is in relation to a dividing line. For example, Calhoun County, MI (Battle Creek and surrounds) label their east-west running roads as lettered drives. There is both A Drive North and A Drive South, B Drive North and B Drive South, etc. They are lettered up and down from Division Drive. Fortunately their address baselines are the west and south county borders, so they don't have addresses like "East 100 A Drive North" and "West 100 A Drive North".
Many counties in Indiana have those "dual directional" roads just like you mentioned, arranged in a grid incrementing by 100 to the mile. Addresses are formatted as #### [Prefix Direction] [Road Number] [Suffix Direction], where the prefix direction indicates the position of the address along the road, while the suffix direction signifies the location of the road relative to the baseline. The addresses increment by 1000 every mile, such that, for example:
*"West 400 North" runs east-west, 4 miles north of the north-south baseline, and is west of the east-west baseline.
*"North 500 West" runs north-south, 5 miles west of the east-west baseline, and is north of the north-south baseline.
*The addresses "5000 West 400 North" and "4000 North 500 West" would both be found at the intersection of the aforementioned two roads.
Personally, I've always found that system rather fascinating, ever since I first saw those grids of county roads - first on Microsoft Streets & Trips, and then on Google Maps.