Milkshakes and malts evolved from the ice cream soda
The milk float, which consisted of ice cream floating in a glass of milk flavored with syrup, was the oldest documented variation of the milkshake. Malted milk was a distinct beverage that had flavored milk fortified with the substance, which was thought to be a digestive benefit (read laxative). The first malted milk shake was made in 1922 by a soda jerk employed by Chicago's Walgreens Drug Store who blended their malted milk beverage with ice cream. The combination was so well-liked that "Malt Shop" eventually replaced "Ice Cream Parlor" as the preferred location for ice cream pleasure.
Without malt, milk/ice cream drinks gained a variety of regional names, such as frappes in New England, egg creams in the South, milk shakes or shakes in the Midwest, and frosted, among others; practically all of these drinks could be purchased by going to a malt store. They were quickly prepared in the presence of the consumer using specialized blenders.
It's interesting that milkshakes and malts never experienced the sniffing contempt that was once reserved for sodas. The original milkshake was a concoction of whiskey, milk, and egg. Shakes became commonplace in the 1960s thanks to the American fast food industry, and they continue to be a uniquely American invention today.