These are notably all vertebrates when in fact the most populous species of animals by far are those of nematodes and arthropods and probably some other lineages that are not Craniates
Can you accept rat or mouse? "Rodent" is an order which covers everything from a capybara to a shrew. Since you distinguish between cows and water buffalos or horses and donkeys in previous questions, it's hard to intuit that you're asking for the entire order name for the last question. Thanks.