Here is more than you ask for about jam and jelly :-) (Though when talking about PB&J, I doubt that people worry too much about the technical details when they're trying to talk through the PB stuck to the roof of their mouths!)
From
http://www.howstuffworks.com/question84.htm
Question
What is the difference between jelly, jam and preserves? And what exactly is Jell-O?
Answer
Jelly, jam and preserves are all made from fruit mixed with sugar
and pectin. The difference between them comes in the form that the fruit takes.
In jelly, the fruit comes in the form of fruit juice.
In jam, the fruit comes in the form of fruit pulp or crushed fruit (and is less stiff than jelly as a result).
In preserves, the fruit comes in the form of chunks in a syrup or a jam.
Pectin is an undigestible carbohydrate (fiber). It is found in the cell walls of most fruit. When heated with sugar in water, it gels, giving jam, jelly and preserves their thickness.
Jell-O is entirely different. It is made from gelatin, which is a protein made from animal skins and bones.