Correct or accurate information?

Correct and Accurate are synonymous. Though 'correct' has a broader meaning. For example, consider the following two statements:

  1. Thugs ran away in a car.
  2. Thugs ran away in a blue sedan.

Both of the above statements provide correct information, but the second statement is more accurate. That's why 'accurate' is more commonly used with 'information'. One can also go for 'precise'.