Natural numbers are counting numbers or their equivalents:
1, 2, 3, 4, 5, 6 .......
Whole numbers are counting numbers and zero:
0, 1, 2, 3, 4, 5 ......
Integers are positive and negative whole numbers and zero:
..... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 .......
Look at this diagram which summarises this.