The first, and most significant difference, lies in how the two places approach what children learn in school.

Due to the 10th Amendment of the American Constitution ("The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.") and the fact education isn't explicitly mentioned, the content of what children learn in schools is the United States is decided at a state level. What this means in a practical sense is that American teachers approach the events of the Colonial era based on how their state approaches the topic. These decisions at a state level are, unsurprisingly, deeply informed by geography. That is, students in the original colonies are much more likely to spend considerable time on the Revolutionary War as field trips to forts and battlegrounds are a practical option. Those states are also more likely to have a long history of public education which means the Revolutionary era is part of the grammar of most East Coast schools. Some Massachusetts and New York State schools, for example, were using textbooks in the early 1800's that included causes for the "American Revolution." Meanwhile, some mid-west states didn't have a public education system in any meaningful sense of the word until the 1910's. Finally, although western states include the The Revolutionary War in their standards, schools and teachers are more likely to spend more time on history that is unique to their region, such as the concept of Westward Expansion, the gold rush, and Catholic Missionaries.

In the modern era, UK's approach is based on a national curriculum. The Education Reform Act of 1988 established the goal of creating a national approach to history instruction, which meant by 1995 or so, most school children in the country would study "The American War of Independence" as a part of the national curriculum. Prior to that, the exact nature of what children studied about one of the former colonies varied from region to region, school to school. The general pattern, though, was one described as "traditional" history or the historical "canon" AKA a history organized around the events and decisions of dead, white, British men (occasionally women). In that context, the presentation of the War was often tied to the school's, or even teacher's, philosophy. In some cases, some schools followed a century rule - they didn't teach anything about British history that happened within the last 100 years. Others taught "kings and queens" history which focused on the actions of rulers, making events they were involved in secondary to the ruler. So, in effect, the American Revolution was something that happened during George II's reign (Haydn, 2012).

Finally, it's worth noting that American educators in the early 1900's were asking similar questions to yours. The turn of the century in the states marked the rise of educational committees and the creation of professional, educational associations. One such group, a committee within the larger National Education Association, posed the same question as you and reached out to various historical groups to better understand how British historians viewed the Revolution. You can read one such take from 1905 here. Part of the reason they were asking was around language. That is, what's the best way to frame that period of history? Was it more about a revolution or more about independence? England has settled into calling it "The American War of Independence" while New York State standards have long referred to it as the "Colonial and Revolutionary Period", "The Revolution", and the "Revolutionary War." Meanwhile, Texas has landed on the "American Revolution" which is a different sequence of events than the "Texas Revolution."

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Haydn, T. (2012).Longing for the Past: Politicians and the History Curriculum in English Schools, 1988-2010. Journal of Educational Media, Memory, and Society, 4(1), 7-25.

Schlesinger, A. M. (1919). The American Revolution Reconsidered. Political Science Quarterly, 34(1), 61-78.