An engagement ring is given when there is a proposal of marriage. Usually it is a diamond, but I have seen many other gemstones given. A popular stone is a Sapphire because of its worth and durability.
A wedding ring is given on the day of the actual marriage. The couple will exchange wedding bands. They are usually a band of gold or platinum.
An engagement rings to me always symbolized a promise. Sometimes the man picks out the ring, sometimes the couple picks out the ring together. Often times a ring will be passed down (which I feel to be the most special. )