As nouns the difference between copse and hedge
is that
copse is a thicket of small trees or shrubs while
hedge is a thicket of bushes, usually thorn bushes; especially, such a thicket planted as a fence between any two portions of land; and also any sort of shrubbery, as evergreens, planted in a line or as a fence; particularly, such a thicket planted round a field to fence it, or in rows to separate the parts of a garden.
As verbs the difference between copse and hedge
is that
copse is (horticulture) to trim or cut while
hedge is to enclose with a hedge or hedges.