The reasons for the difference, I'd argue, are based on the economics of the regions they colonized and the segregation of colonists and indigenous peoples in the Americas.

The Iberians were looking to make the indigenous peoples of what is now Latin America subjects, to convert them to Christianity and make them work for the crowns of Spain/Portugal. In Columbus' letter to the king and queen of Castille and Aragon, he implied that the people of Hispaniola were to be servants of the crown of Spain or God (or both). This went hand in hand with Iberians colonizing these regions. Though African slaves were initially preferred and the majority of African slaves in the Americas reached Latin America, it was expensive to get African slaves to, say, Lima or into the Amazon. It was more economically viable to use indigenous peoples for work in territory they already lived in, cutting costs or transportation and the indigenous peoples there were already familiar with the land.

England (and by extension, France) in modern Canada and the Great Lakes region were more focused on trading fur, either in factories established in indigenous territory or directly in indigenous camps. The indigenous people of the North were needed away from the colonies due to their importance in the fur trade. The first nations were relied on to gather the furs and then trade them with French and British traders.

The economy of the colonial US, specifically the southern US, was based on African slave labour on plantations and farms rather than indigenous labour. In New France and British North America, First Nations people were largely segregated from colonists and therefore any "fraternization" that happened was on a smaller scale than Latin America, which mainly was limited to trappers and indigenous women in the north. I don't know about the US though I'm more familiar with Canadian history, but there is a sizable group of indigenous and European people called the Metis in Canada.

TL;DR indigenous people lived apart from colonists in British and French lands due to the economies of those colonies.