One of the comments to Stephen Wolfram's blog post on Ada Lovelace, mentioned that WolframAlpha (verified in Mathematica as well) provided slightly different results for the question of Ada's age when her father, Lord Byron, died, if the question was asked in two different ways.
Using "death of lord byron - birth of ada lovelace" gives 8 years, 4 months 22 days, while "age of ada lovelace when Lord Byron died", gives 8 years, 4 months, 9 days.
On expanding the details in both answers, the resulting dates used to calculate the answer are the same. Where does this slight difference come from?