Crown Reduction is the removal of branch wood from the complete crown. Typically, 10-30% of each branch is removed to give an overall smaller size. This is carried out when trees outgrow the positions in which they are planted.
Crown Lifting is the removal of lower branches to improve ground clearance and allow access (in this case to allow a tractor access for mowing).
Crown Thinning is the removal of branches within the crown, to enhance the shape and balance of mature trees. Weak branches or those that are misplaced are removed. This would also include any damaged or diseased wood. Thinning will also reduce wind resistance. Shading will also be reduced.