Something to note :

Whole numbers start from 0 onwards.
Natural numbers start from 1 onwards.

To say that an integer is a 'whole number that can be positive, negative or zero' is strictly speaking, wrong by definition.

Eg. -5 is an integer but not a whole number or natural number.

Whole numbers can never be negative by definition. However, we can say that numbers like -5 or -100 are negatives of the whole numbers 5 and 100 respectively.

The following sentences are more accurate definitions of 'integer' :

① Any of the natural numbers, the negatives of these numbers, and 0

② A number with no fractional parts (or decimals)

③ A number that can be written without a fractional component.