It is a definitional thing. Counting numbers are whole numbers (integers) starting with 1.
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Nothing, except whole numbers include 0 (zero) while counting numbers start with 1 (one)
If a timer is counting down from 30, it doesn't actually count 30. It starts counting at 29. If you are counting up to 10, you wouldn't count the number that you are counting from. If you counted 0, you would actually be counting 11 numbers.
zero is not a counting number. if you count the number of kids in a room, would you start with the number 0?
They are not. 0 (which is a whole number) is not considered a counting number(natural #).