"I absolutely love her!" = It might mean love her as much as is possible "I definitely love her!" = means that I'm sure I love her, but it doesn't indicate how much. Definitely usually has more to to do with certainty, and absolutely usually has more to do with amount. "I absolutely hate this band, and I'm definitely sure I don't like them" = I hate this band the most possible amount, and I'm sure I don't like them."

There is no difference that I can think of; they're basically perfect synonyms. "Absolutely" may possibly be used in place of "definitely" because it sounds a bit more emphatic to a native ear, but that's about it.

Like Okaydaniel said, "definitely" has to do with certainty. You are sure about something. For example, "I'm definitely going to buy that product" or "she would definitely know the answer". "Absolutely" has two meanings: one is the same as "definitely" (in this case they are synonyms so you can use either one) and the other meaning is "completely". For example, "That dress is absolutely gorgeous" or "They are definitely right"

Hope this helps: "Absolutely is totally not definitely" http://itre.cis.upenn.edu/~myl/languagelog/archives/002022.html