Interesting to bring distinction. I think it's equally important to understand specific definition, but also acknowledge more colloquial application of the words and how we apply them.

I think when one says, "that woman is displaying racism in what she says", it is intended, or at least meant to be construed in a particular context of both colloquial prejudices and racism. Her prejudices, which as pointed out in the video are seeming to be based on things that she is not fully aware of or acknowledging as racist. It is not to be implied specifically that she is a "racist" i.e. believing in racial superiority as walking belief. For all we know for that matter, we can assume she is just a woman, perhaps a mother, a wife, a worker who is just trying to live her life in the best way possible.

If we look to the specific definitions of both words as you note them, we can see both with some implication of intent and awareness in the use of the word "belief". This seems to hold that one has measured their understanding of the world and then utilized their belief in action.

More tangent, why racism and prejudices are so difficult (in my opinion) is because there are very few things in our lives that we measure so carefully as to make conclusions like this. Likely most of us are much more prone to impulse action and reaction.