They can mean the same thing, but they are used in different ways. I can use 'determine' to mean establish or discover. "Using the clues provided, the detective determined who the killer was." You would not see 'decided' used here. 'Determine' is used more if there are objective facts involved, though 'decide' could also be used. 'Decide' is used when a choice is subjective. "He decided not to go." "She decided on the red dress for the dance." You would not use 'determine' much in either of those two cases.