There is a specific history of anti-Black racism, though.
“Race” pre-1492 was largely in Europe defined on the basis of religion - either you were Christian, you had not yet heard the word of Christ, or, worst of all in this view you had the opportunity to accept Christ but rejected him (Jews and Muslims) which also meant “just war” could be waged against you. Racism in this sense was wielded against Jewish people inside Europe, and Muslim people abroad in the crusades (as well as Moorish Spain.)
When contact is made with the Americas, initially this schema of Christian souls is transferred onto Indigenous people. Las Casas and Sepulveda hold a famous debate in Spain where Sepulveda argues the “Indians” are “barbarians” (using Aristotle) and therefore just war can be waged against them. Las Casas argues the Indians do have souls, and can be Christianized and also testifies a great deal about the violence and genocide being enacted. Of course, there’s money in the “New World” so the “Indians” continue to be slaughtered.
This Christian/non-Christian scheme is also transferred to African people, justifying slavery. As Locke writes, a captive taken in war can be enslaved, and if is also moral to enslave someone who rejects the word of God - to Christianize them. This justifies enslavement.
As we begin to enter the “Age of Enlightenment,” the discourse shifts from souls to reason. Kant argues that man is defined by reason - an important move into secular thinking. But Kant also was immersed in deeply racist literature and travel narratives and also explicitly believed that that reason only belonged to white European men. This begins the creation of a human scale with white men at the pinnacle, and African people specifically as the opposite - lacking reason and humanity, and beast like.
With the advance of evolutionary theory and biology, those theories are used to categorize and hierarchize humanity. Races begin to be explicitly categorized and labeled and assigned characteristics - this is the birth of “scientific racism.” Different races are given different characteristics, with Black people inhabiting the bestial. It is not that racism doesn’t exist against other races at all - the history of colonization around the globe shows us that - but in this categorization of the human, Black people come to stand in as the absence of the human - the most primitive, the most beastial, the most horrific, the least intelligent.
In Orientalism, Said traces the way the European imagined the “orient” which says more about Europeans than Asian/Middle Eastern people. The “East” was simultaneously seen as exotic and barbarous, infantile and dangerous. Hegel in the Philosophy of History says “Africa has no history. Let us pass over it.” Asia, meanwhile has a “nature” that is barbaric and despotic. Both are racist, but with different impact - Africans aren’t even part of human history. In the late 1800s in particular as exclusionary immigration bills are passed the UK, US, Canada etc to exclude Asian migration, criminal panics and the idea of Chinese as sinister opium dealers emerge. These exclusionary laws are also passed against Jewish people.
This is a very capsule tracing of complex ideas, but the reason for specifically identifying anti-Black racism is that racism is conceived differently for different groups. “Asians” find themselves inhabiting model minority narratives that stereotype them (robotic, emotionless, good at math and science but lacking creativity, interchangeable, smart but no personality, not good leaders, submissive exotic women, sinister and sneaky, etc.) This is racist and damaging but distinctly different from the way racism acts towards Black people - sub-human, not intelligent, bestial, hypersexual, criminal. So in order to not lump these distinct histories together, people identify “Orientalism” as the distinct ways Asian/ME people are seen, Islamophobia for the ways Muslims are seen as terrorists, barbaric etc., anti-Black racism for how Black people have been specifically seen outside the human. Just saying “racism” often means that the people deemed lowest on the human hierarchy - Africans - are ignored (saying “racism” in schools for example won’t capture the specific ways Black students are seen as unintelligent, low achieving, discipline problems, from pathological families and cultures, etc.)
Through the 19th C in particular, anti- Semitism actually argued Jewish people were too civilized and cosmopolitan. While Africans and the “natives” around the world were seen as primitive and savage, Jewish people were seen as hyper-civilized (controlling banks, insidiously infiltrating government, global conspiracy, etc.) If race mixing was to be feared for lowering the white human race, Jewish people were dangerous because one might not know they were Jewish and they could infiltrate. While natives needed to be civilized, justifying colonization and slaughter, Jewish people represented the opposite pole - the fear that (whenever whites lost against their opponents) Europeans were becoming too soft and feminized (the crisis over the Boer War for example.) This tension - whites are the only civilized people, but civilization makes you weak - is one of the ironies of white supremacy. Jews, seen as hyper-intellectual, physically weak, and infiltrators of the nation, become the scapegoats for this anxiety.
These racial ideas were also protected onto Irish people, Scottish people, working class whites, miners, Eastern Europeans at various points. Whiteness as we understand it is a recent, late 19th C construction - in response to internal and external threats to Empire - “ whiteness” is expanded to accept Irish people, Slavs, etc. who would previously have also been seen as lower people.
But while Irish etc get absorbed into whiteness eventually, Black people are always seen as the opposite pole from white humanity. The structure of race itself rests on this supposed fundamental opposition of Blackness to white humanity. In the hierarchy, Blackness rests firmly at the bottom. These conceptions brought to us through the Age of Reason, solidified by slavery and science and law, continue today to label Blackness as outside the human. Which is why specifically understanding anti-Black racism is necessary in understanding the history of constructing race, period.
So Abbott expressed herself badly and ignorantly - racism doesn’t just exist for Black people, but she’s not wrong in recognizing that we can’t address racism as one lump, it has specificities in history and contemporary life for each group.