No. All whole numbers are integers and all integers are whole numbers.
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It depends. Some authors consider "Whole Numbers" to be the positive integers, some consider them to be the non-negative integers, and some consider them to be all integers. For the first two definitions, numbers like -3 would not be considered "whole numbers". With the last definition, negative numbers like -3 would be considered a "whole number".
The set of integers is the same as the set of whole numbers.
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 answer below is incomplete.The set of whole numbers also includes all negative integers.
Integers include 0, the negative numbers without fractional parts, and the positive numbers without fractional parts. The "without fractional parts" part of the description implies that all of the integers are whole numbers. Therefore, if you are adding integers, you are adding whole numbers.