Highly debatable. One can call something whatever one likes, but most technically the left image is not “America,” but “The Americas.”
North and South America are on separate continental plates- they are not a singular continent. Central America does not have its own plate, it is on the Caribbean plate mostly, and parts of some “South American” countries are also on the Caribbean plate as well. There are some more plate issues we could bring up- but if we are using continents or continental plates as identifiers we cannot accurately say that all the land shown in the left image is “America.” Of course by name, or at least the name in several languages, we could say they all have america in the name- but so do some places not shown in the left image, and anyone can use the name “America” if they chose to do so. As far as culturally- this is again problematic as language and culture can vary greatly among the peoples, indigenous or otherwise, in the lands shown to the left.
North and South America are on separate continental plates- they are not a singular continent. Central America does not have its own plate, it is on the Caribbean plate mostly, and parts of some “South American” countries are also on the Caribbean plate as well. There are some more plate issues we could bring up- but if we are using continents or continental plates as identifiers we cannot accurately say that all the land shown in the left image is “America.” Of course by name, or at least the name in several languages, we could say they all have america in the name- but so do some places not shown in the left image, and anyone can use the name “America” if they chose to do so. As far as culturally- this is again problematic as language and culture can vary greatly among the peoples, indigenous or otherwise, in the lands shown to the left.