What is the difference between adding whole numbers and adding decimals?

The main difference is that with whole numbers the decimal point is "hiding" (after the last digit of each whole number) whereas with decimal numbers it is clearly visible.

In both cases the numbers are added with the decimal points aligned - with whole numbers there are no digits after the decimal points so the decimal points are not written, but if they were they would be visible after the last digit of the whole numbers and they would be automatically aligned; with decimal numbers there may be a different number of digits after each decimal point so it is up to the person doing the arithmetic to ensure the decimal points are aligned.