What you've said is technically correct (the best kind of correct). But the word cattle is also used to refer to other similar animals such as Yak, Bison, Buffalo.

Merriam-Webster defines cattle as

: domesticated quadrupeds held as property or raised for use
specifically : bovine animals on a farm or ranch

Cambridge defines it as:

a group of animals that includes cows, buffalo, and bison, that are often kept for their milk or meat

And Oxford as:

cows and bulls that are kept as farm animals for their milk or meat

Wikipedia is more specific and defines it as:

Cattle or oxen (Bos taurus) are large, domesticated, bovid ungulates. They are prominent modern members of the subfamily Bovinae and the most widespread species of the genus Bos.

Not disputing your fact at all, just clarifying that words often have multiple meanings and meanings also change over time according to popular usage, so saying cattle means livestock isn't necessarily wrong, it's just not as precise as the technical definition. And the more people that use it that way the more correct it becomes. As I dove deeper into the topic, I'm seeing evidence that suggests that Cattle is also an American term that means Livestock, but is marked as archaic. Which honestly makes sense as the word's etymology is the following according to Merriam-Webster:

Middle English catel, cadel "property (whether real or personal), goods, treasure, livestock, (in plural cateles) possessions," borrowed from Anglo-French katil "property, goods, wealth," borrowed from medieval French (dialects of Picardy and French Flanders) catel, going back to Medieval Latin capitāle "movable property, riches," (in Anglo-Saxon law texts) "head of cattle," noun derivative from neuter of capitālis "of the head, chief, principal"

Anyway, good fact nonetheless.