Dill is the only member of the genus Anethum. The flower heads and seeds are used for a wide variety of culinary purposes, including soups, fish and seafood dishes, breads and pickling. The leaves are slightly thinner, more delicate and feathery than fennel.
Fennel is a member of the genus Foeniculum. Fennel's large edible fennel "bulb" is located just under the ground. This is not a true bulb, but is formed by the large base of the plants leaves. Cooks use this bulb, foliage and fruit (often called seeds) in salads and soups, and it is an important herb in Italian cuisine. Fennel has a licorice-like smell and flavor similar to anise.
Since fennel and dill are in the Umbrelliferae family, most botanists believe it is possible for them to cross-pollinate. If you grow both, you should plant them as far apart as possible and should take care to hand pollinate both plants to cut down on the chance that your plants will cross-pollinate and produce a hybrid plant.