Ice cream is a catchall term for frozen dairy desserts, and the exact definition varies from place to place. Wikipedia describes ice cream as "a colloidal emulsion made with water, ice, milk fat, milk protein, sugar and air." In other words, it is foam. Ice cream always contains flavoring of some sort. In the United States, in order for a product to be labeled "ice cream," it must have at least 10% butterfat, and 6-10% milk solids by weight. Percentage by volume is meaningless because air is whipped into the cream to make it scoopable.
Frozen custard is made with egg yolks, and is often labeled as ice cream as long as it otherwise meets the definition. The addition of egg yolks keeps ice cream from melting as fast as it would otherwise.
Gelato is an Italian term that simply means ice cream. In the US, it is distinguished from ice cream by having less butterfat (6-9%) as it is made with more milk and less cream, and gelato has less air whipped into it. While both ice cream and gelato may contain egg yolks, gelato will have fewer or none at all. The result is that ice cream tastes like cream with a flavoring, and gelato tastes like its flavoring with a bit of cream. Gelato is also denser than ice cream, and will melt faster.
Sherbet is made of water, milk, sugar, and (usually fruit) flavoring. The amount of milk is not important to its definition, and early recipes sometimes used egg whites or gelatin instead of milk.
Sorbet is a frozen dessert made with ice and fruit, with no dairy products. The fruit can be juice or pureed fruit, but sorbet can also be made with liqueur or honey sometimes.
Ice milk is made the same way ice cream is made, with plenty of air and sugar, but much less butterfat. The term ice milk has fallen out of favor, and this product is now usually labeled as "frozen dairy dessert."
Pinning down the history of ice cream is difficult because frozen sweets have been traditional in many parts of the world for thousands of years, and how you define your terms makes a difference.
If the idea of gelato is giving you a craving, Metafilter has a roundup of links on where to find the best gelato or even make it at home.
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