How do you discern between the two?

Again, it depends. I don't think a general answer to that question exists. With studies, I suppose?

In order to study something, we must first define the variables.

How would you define race vs. culture?

To clarify, "racial differences" generally meant "genetic differences". So a better way to put it is not race vs. culture, but genetics vs. culture, as ethnic groups (or more broadly speaking, races) can have both different genetics and different cultures. In other words, nature vs. nurture. You take people of different races, look at the differences between them and then study how much of the variations are due to genetic or environmental causes. "Racial differences" I guess could mean both genetics+culture.