The difference has to do with the concept of "thinning and heading" and how plants respond to abiotic damage. Thinning refers to the removal of a branch or shoot all the way back to the node which it originated from. This is the primary type of pruning used on trees - either to limit growth or to increase the amount of light permeating to lower branches. Late winter is generally the best time to do this, just before the tree breaks dormancy, since plant pathogens are generally less abundant. By pruning in late winter, this also reduces the amount of time that the wound is exposed before the tree begins active growth.
In contrast, "heading" refers to the partial removal of a branch, usually 1/2 to 1/3 back to the node. The purpose of heading is to stimulate shoot growth on the remaining branch - hedges being a primary example. Because new shoots and leaves are desired, heading is usually performed at the height of stem growth (in most climates late spring to early summer).
The biologic processes behind this are complex (botanists are just beginning to understand how plant behavior adapts to predation) but in very general terms, plants respond to damage in two ways: by compartmentalizing the wound; and by stimulating growth on the remaining tissue. Many types of woody plants produce latent (or adventitious) buds, which lie dormant within the cambium tissue. Normally these buds are suppressed by auxin hormones produced in the meristem by active shoots. When the meristem is removed (such as through heading the branch), these buds rapidly develop to produce new shoots and leaves. Most species used for hedges are selected because of this ability.
So long story short: thinning is best performed in late winter, when the plant will quickly be able to seal off the damage while limiting the production of unwanted water sprouts and suckers. In contrast, heading is usually done in early summer, when the hedge can vigorously produce new growth and fill out any gaps.