One textbook from which I have taught (Out of Many, by Faragher, et.al.) characterizes the difference between these two as the difference between a “frontier of inclusion” and a “frontier of exclusion.” The latter refers to British relations with the Native Americans while the former refers to those of the French.
The French brought relatively few settlers to the Americas. They did not try to occupy and farm the land. Instead, they generally traded with the Indians. The French colonial economy was based largely on trading for furs. For this reason, the French needed the Native Americans and generally got along decently with them. They often intermarried with them and created a society that generally included Native Americans.
By contrast, many British settlers came to North America. They were there to farm and to create their own new society and economy, not to trade with the Indians. Because the British were there to farm, they needed land. The need for land led to conflict with the Indians. The British and Indians, therefore, never really tried to merge their societies in any way. This was a frontier of exclusion.