What are the differences between fruits and vegatables, what
characteristics are used to classify them?

Here's a straightforward answer from a UK science site:

"Fruits are or contain seeds, they develop from the ovaries. Nuts,
olives, tomatoes, peas and runner beans are all examples of fruits, as
well as the obvious ones like apples, oranges and grapes. Vegetables
are non-seed containing plant matter. They include leaves, such as
cabbage, lettuce or watercress; roots, e.g. carrots or beetroot;
bulbs, like onions, and tubers such as potatoes."

"What is the difference between fruits and vegetables?"
ScienceNet
http://www.sciencenet.org.uk/database/Biology/9608/b00616d.html

And here's a question-and-answer web page with a similar description
of the difference:

"A fruit is the matured ovary of a flower, containing the seed.  ... 
A vegetable is considered to be edible roots, tubers, stems, leaves,
fruits, seeds, flower clusters, and other softer plant parts."

This page also explains that a grain is a fruit, while nuts are a more
complicated matter.

"What's the difference between fruits and vegetables?", SDSTAFF Terey
Straight Dope Science Advisory Board
The Straight Dope
http://www.straightdope.com/mailbag/mveggie.html

For further information, you can consult these web pages from Cornell
University:

Q: What is the difference between a fruit and a vegetable (or Is a
tomato a fruit or vegetable)?"
Cornell University: Department of Horticulture
http://www.hort.cornell.edu/extension/question.html#1

"The difference between fuits and vegetables" [sic]
Cornell University: Division of Nutritional Sciences: Nutriquest
http://www.nutrition.cornell.edu/nutriquest/070599/fruitveg.html

- justaskscott-ga


Search term used on Google:

"difference between fruits and vegetables"

Very good answer, did not realize how confusing everyone is on the
topic, there was even a ruling by the Supreme Court!  Overall was very
good research, a job well done.