It is understandable that a white person experiencing anti-white attitudes on the part of Blacks would feel unjustly maligned however, anti-white attitudes or anti-white racism is not the same as institutionalized racism, a pervasive problem in American society that resulted from legalized slavery being permitted and written into America's earliest foundational documents and institutions. 
So to answer your question, yes, racism (reactions of non-whites to whites that result from institutionalized racism) on the part of Blacks or other non-whites, is different from institutionalized racism a.k.a. white supremacy--a pervasive and defining feature of American society that continues to pervert American democratic ideals.