I'll take a stab at it. Took part of my PDC from Darren Doherty!

But this is strictly from memory ... I'll have to dig out my notes to verify, so correct me if I'm wrong. I'm looking at this as a "pop quiz"!!
The keypoint is located in the folded, "drainage" area of a hillside (i.e., where a creek might flow) and occurs at that point where the slope of the hill transitions from convex to concave. The keyline is the contour line that runs through this keypoint (it's on-contour).
Keylines are "plowed" using the chisel plow (Yeoman's plow) parallel to the keyline. As the slope flattens out in the concave portion, these plowed lines
are not on contour but instead slope downward to the vertical ridgelines. Keyline plowing is a method to distribute water from the drainage areas of a hillside to the dryer vertical ridges which are typically dry. The chisel plow lifts and uncompacts the soil allowing free water movement without disturbing soil's surface which would cause erosion. These keylines would allow you to plant your trees and shrubs across the entire hillside and ensure they get sufficient water even out on the ridges. Without them you might be limited to the drainage area only. (see Water for Every Farm - Yeoman's Keyline Plan)
Swales are by definition always on contour, and as such are not necessarily parallel to each other. Swales are for slowing water flow down a hillside and infiltrating it into the soil high in the landscape. Swale and keyline have similar purposes but different methods.