How do jelly, jam, and preserves differ from one another?

Fruit preserves are simply fruits that have been prepared and packaged for long-term storage. The preparation of fruit preserves traditionally involves the use of pectin as a gelling agent, although sugar or honey may be used as well.
 
Jams are preserves made from fruit juice, pectin, and pieces of the fruit's flesh. The fruit is heated with water and sugar to activate pectin in the fruit.
 
Jellies are  made from fruit juice and pectin. They are made in much the same way as jams are, though an additional step filters out the fruit pulp.
 
The FDA regards jam and preserves as synonymous, but distinguishes jelly from jams and preserves. Jelly  is made entirely from fruit juice or other liquids. Jams and preserves are gelled fruit that may include the fruit's seeds and pulp.
 
Pectin is a natural substance in fruit that causes the fruit juice to gel. Commercial pectins are made from apples or citrus fruit.
 
Some fruits contain sufficient amounts of natural pectin to gel firmly. Others require additional pectin. Fruits containing sufficient natural pectin to form a gel include crab apples, tart apples, sour blackberries, sour boysenberries, plums, cranberries, lemons, and wild grapes. Fruits low in pectin include cherries,  ripe blackberries, grapefruit, grapes, melons, and oranges. Fruits that always require added pectin when making jelly or jam include peaches, pears, elderberries, strawberries, raspberries, grapes, guava, and pomegranates.
 
Source(s):
Wikipedia "Fruit Preserves"
Welch's "Frequently Asked Questions"