Race? Or Racism?

Is race a socially constructed concept? A social construct is defined as an idea or notion that appears to be natural to people who accept it but may or may not represent reality. Thus, it remains largely an invention of a given society. Race is defined as the major divisions of humankind, having distinct physical characteristics. Even if society has a different idea of race, race will always be the major divisions of humankind based on biological differences. In that sense, race is not a socially constructed idea, as it is not subject to change. Racism is defined as the belief that all members of each race possess characteristics or abilities specific to that race. Racism goes beyond the hard-bordered physical distinction of human beings and tries to differentiate humans by their assumed mental characteristics. Physical characteristics, such as skin color, are not directly linked to mental characteristics, yet society tries to falsely link them together and therefore race becomes a socially constructed concept. An example of this can be seen here, from Maus (p. 50):

The German soldiers couldn't even recognize a German from a Jew, even though they had a "defined" system of distinguishing Jews from other people. The idea of racism is subjective to the core and is inefficient as a means of classifying people. Racism shouldn't be confused with the concise definition of race, which it commonly does in today's society. The assumptions we make about people purely based off their looks should be understood as they are, assumptions.