I don't think it an easy thing to grapple with because if one person attacks another based on difference, it's important to know what they perceived.
Ethnicity is not precisely the same as race, but does a racist thug care about the distinction before they give someone a kicking? I think probably not.
Race used to be just thought of belonging to or from a place. But the big melting pot has changed that. Race, nationality, ethnicity, religious belief all inextricably intertwined.
Under common law, what Abbott said is more aligned with ethnicity than race. However we don't have a single simple word like 'racism' for prejudice on the basis of ethnicity. The courts have ruled that Jewishness is an ethnicity, where others may think of it as a religion. A British Jew therefore has two identifying characteristics, so if beaten up by thugs when abroad, the attack could be racially motivated because he is British, but then if they are beaten by people from some other faith, then the attack is motivated by some anti-ethnic sentiment.
So I think the only available word is 'difference', and if we put 'difference' into working for a definition, then we'd be on our way. But then because people share a language, or a culture, then any definition will need to encompass that too.
Who thought it would be easy?