Plain Sawn: The log is canted (into 4 flat sides) and milled by equally rotating the log to relieve tension. Grain typically runs near horizontal through the board

Live Sawn: The simplest of milling - the log is simply cut through from top to bottom. 

Rift Sawn: A fairly desirable grain pattern. The grain runs between 30 and 60 degrees (approaching vertical) through the board. This helps stabilize the lumber and mitigate warping, cupping, and twisting. 

Quarter Sawn: The highest quality and most sought-after lumber. The grain runs between 60 and 90 degrees (vertical) through the board - with 90 degrees being optimal. This is the strongest and most stable lumber - resisting twisting, cupping, and warping.