The difference between these maps and map videos is that the action all takes place on the map. On an animated map, you see borders change, troops advance and retreat, and empires grow.
The biggest and best collection of animated maps I know is called The Map as History. Their collection includes 250 animated maps, a number they assert is the largest on-line collection available. The maps are divided into 16 collections, most of which are better for World History, but these collections would be excellent for US History teachers and students: The United States: a territorial history (with 21 animated maps), and The Cold War library (with 9 maps). A new library about North American colonies currently has four maps but eight more are being developed.
The Map as History is a subscription service and the yearly fee for each series is about $12 a year for one collection, or around $55 for the entire series. What is great, though, is that they allow you free access to some maps as samplers, such as this animated map (4:17) of Nouvelle-France (New France) and this animated map (4:12) of antebellum expansion.
My second favorite animated map collection is by Western Heritage Mapping. These maps are all free, and they focus on military battles and wars. For example, they have an animated map of the Battle of Antietam, and this one of the War of 1812.
Because they're so different, it's not a matter of choosing one over the other. Both are very valuable additions to our teacher tool kits.