Culinary definition of stir: To use a circular round-and-round motion to mix ingredients with a spoon or implement.
C@H FOOD FOR THOUGHT
More-or-less the same as mix but conventionally used primarily to describe fluid mixtures that turn over or move easily, rather than dense mixtures that require more resistance to move - ie: 'stir the soup or the applesauce (right)' and 'mix the cake batter'.
Stirring may refer simply to moving food to avoid burning etc., whereas mixing refers to the action of moving ingredients to incorporate.