Having read RiMmer's excellent distinction, I'd say that, outside science, these words are sometimes interchangeable, but not always; where they are contrasted, I believe the distinction often hinges on intention (focus/method: precision) versus result (success/failure: accuracy).
If you are precise, you display attention to detail as much as you can, i.e. you do your best within the limited range of your abilities to be precise. But whether you are successful may also depend on other factors beyond your power.
Embroidering cushions is very precise work.
Work can only be precise: accuracy wouldn't be quite appropriate, because failure is hardly relevant or even possible. A good result is taken for granted, because it is well within one's abilities to succeed.
She calculated precisely how much sulphur she would need according to the formula to make gold.
She does what she can; but will she make gold? This sentence says nothing about success or failure.
If you are accurate, you produce results that are close to your target; whether you tried hard and did your best is irrelevant.
She calculated accurately how much sulphur she would need to make gold.
This implies that she successfully calculated how much sulphur she needed.
Your prediction of 1–2 % economic growth was accurate, imprecise though it was. You were right; but next time please provide a more precise estimate.
This is not to say that they always differ on this point; sometimes they are equivalent; and sometimes precision isn't so much about intention as it is a neutral opposite to blurred or general. But I do believe accuracy is mostly about result.