There are 3 different shapes that are mentioned when training fruit trees.
The vase shape and central leader are more commonly used. Below is a visualization of a fruit trees first few years of growth and pruning to accomplish the vase shape. Both thinning and heading cuts are used to accomplish this.
Thinning cuts are cuts made at the base of the branch you are pruning. Heading cuts are made at differing lengths of the branch. The purpose of thinning is to make the trees growth less compact and open up space for the inner branches to receive sunlight. The purpose of heading is to force growth from buds lower on the branch rather than letting it grow longer.
It is also helpful to understand the difference between leaf buds, flower buds, and spurs on our trees. Flower buds and spurs bear fruit and should not normally be removed, however some branches that need to be pruned may contain a few fruit bearing buds or spurs. Spurs appear on apples, pears, plums, and apricots. Flower buds grow alone or beside leaf buds on stone fruits and with several leaves on apples and pears.
Photo courtesy of Michigan State University Extension
Here is a photo of spurs on fruit trees:
Photo Courtesy of Country Trading Blog
Now that we can identify these let us move on to how the fruit grow on each tree.
Almond: Almonds bear fruit on 1 year-old shoots. They continue to bear on that branch for up to 5 years. Vase shape training
Apple: Apples bear on two year-old wood for up to 10 years. Be careful not to pull off spurs when harvesting. Vast shape training
Apricot: Apricots only bear fruit on the previous years growth. Pruning recommended in late Summer to avoid disease. Pruning keeps production near and not on top branches only.
Cherry: Cherries bear fruit on spurs for up to 10 years. Central-leader system
Peach / Nectarine: Peaches fruit on 1 year-old wood and will not fruit again once harvested. Vase shape training. Prune back vertical shoots to horizontal shoots.
Pear: Pears bear fruit on spurs on 3 to 10 year-old branches for up to 10 years. Careful not to pull off when picking pears! Central-leader system.
Plum: Plums bear fruit on older branches spurs with the best production being from 2 - 4 year-old branched. They bear for 5 to 8 years.
Pomegranate: Pomegranate fruit on new growth each year.
With this information we can identify what branches will bear fruit and consider that when pruning branches.