Tree removal means removing/cutting down the whole tree to ground level. Some reasons why you might consider a tree removal will be its outgrown its environment and a reduction would not solve this issue. It may be dead/diseased meaning its has become dangerous and a safety concern. When performing a tree removal, the arborist will either fell or climb and dismantle the tree depending on its location.

Crown reduction means reducing the trees crown by either height and/or width. Some reasons why you might consider a crown reduction will be to make the tree more suited to its environment, as it might have outgrown it or to reduce the effects of shading and light loss. The final result should retain the main framework of the crown while leaving a similar yet smaller outline of the original leaf bearing structure. 

Hed​ge trimming means to trim/cut back the new growth that has grown since its previous trim. Some reason why you would get your hedge trimmed would be to maintain its shape and thickness, keeping it neat and tidy.
Hedge reduction means to reduce the hedge by height, creating a new hedge line. Some reasons why you might consider a hedge reduction will be to make the tree more suited to its environment, as it might have outgrown it or to reduce the effects of shading and light loss. Hedge reductions are recommended before/after bird nesting season.

Pollarding means to prune/cut the tree smaller than they would naturally grow. It is normally started once a tree reaches a certain height, and annual pollarding will restrict the tree to that height. The final result should be a new framework that the tree can grow from with no leaf bearing branches remaining. This type of pruning can only be tolerated by some species of tree due to its aggressive nature.

Deadwooding is a form of pruning that involves the removal of dead limbs and branches from a tree. Light deficiency, pests and disease damage to root damage are all part of a range of reasons why branches can die off. Deadwooding should be carried out for safety as dead branches will eventually decay and fall off.

Garden clearance means to remove all trees, shrubs and green waste. Some reasons why you might consider a garden clearance will be to clear an overgrown/out of hand so its easier to maintain in the future or to remove everything so you can start over.

Green waste removal means to remove wood, branches, shrub, weeds and grass that have already been cut. All green waste is recycled.