While I agree with you that in the vernacular of common conversation, racism has these different meanings, in the study of oppression, it applies only to the individuals who wield power. Thus, black people would be biased, prejudiced or bigoted, but not racist.
My friend alto has written this up very well.
If I didn’t tell her that in one of my responses to her, that’s unfortunate. I do believe that at least one of my responses to this individual specified that definition. But your comment reminds me that it would be good to put that into all responses so as not to have people confused as to my meaning.