If a branch is pruned just above a side branch, the tip bud on that branch becomes dominant. It is usually the only bud that develops, so there is only one bud stimulated to grow instead of three or more.
If a branch is pruned clear back to where it originates from a larger branch, normally no new branches are stimulated to grow.
To summarize, there are three types of pruning cuts. Each type gives different regrowth results. Pruning just above a bud results in three or more new branches. Pruning just above a side branch results in one branch for each branch removed. Pruning back to a branch origin thins the shrub.
When shrubs are sheared, it stimulates multiple branch regrowth. This results in thicker and smaller growth. We shear hedges because we want thick growth. We also usually want a uniform geometric shape.
In most cases we want shrubs to maintain their natural thickness, so we prune most branches back to a side branch. That keeps the same natural thickness.
When growth becomes too thick, such as when power clippers have been used, then removing whole branches back to their origin is the primary pruning cut.
If one part of a shrub is too thin and open, you may want to tip prune, leaving several buds below the pruning cut to encourage thicker growth. By using these three cuts at appropriate times, you can achieve a natural look on any shrub.