Dave,
Your assessment is correct. One patch of asphalt is really two runways (if designated as so, like 4R-22L). If it's designated only once (like 4R) it may only be used in one direction. Runway alignment and landing aids is done primarily by prevailing weather, usage (type of equipment) and surrounding airport restrictions. (That's why there's a 13-31 at LGA and JFK; a 4-22 at JFK, LGA, and EWR.)
Pilots' "bible" is a book of runway approach plates published by Jeppesen. There's one plate for every runway, meaning two pages for 4R-22L when so designated. It tells pilots what equipment to expect, standard approach/departure paths, frequencies, obstacles, etc. Kind of like track maps for pilots!
And that's (air) Traffic and Weather Together.