While you are right in stating that the difference is ridiculously small, you are wrong to state that the difference is smaller than 10^-999. The reason for this is that your calculator, while able to
represent such small numbers, does not have that much
precision. Most likely it has an internal representation with 12-20 significant digits, most of which it didn't present to you (thus your numbers are the same). This is a possible cause of errors in many computer calculations, but is normally of no real significance.
I think it is possible to get a feeling of the potential actual difference by looking at the number of significant digits in your calculations. Though I'm a little lost in how to explain it
Mosquito