no whole #'s include 0 and counting #'s don't include 0
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They are not. Counting numbers are a proper subset of whole numbers. Negative integers (-1, -2, -3 etc) are whole numbers but they are not counting numbers.
C. whole numbers can be negative and don't match the other sets
Each integer is a whole number and each whole number is an integer. So the set of all integers is the same as the set of all whole numbers. By the equivalence of sets, integers and whole numbers are the same.
The set of integers is the same as the set of whole numbers.
1 and 0 are the two whole numbers with their sum same as their difference