All vertebrae are not identical. For example, certain features distinguish bird vertebrae from mammal vertebrae. The vertebra count for bird necks, as you discovered, varies by group. Birds' cervical vertebrae are uniquely shaped so that two adjoining vertebrae can more easily turn or twist against each other. Other differences are also important.
Owls have an atlas even more favorably shaped for turning the head.
Being able to recognize mammal vertebra types can help a naturalist do a better job teaching people how to interpret owl diets from bones in pellets.