Accurate more or less means correct. Precise more or less means detailed. For example, if you ask me 'How tall are you?', 'About 160cm' is an accurate answer because it's very close to the truth. However, it is not very precise. If I answer '167.798cm', this answer is precise because it is detailed. However, it is not accurate because I am much shorter than this. An answer that is both accurate and precise would be '161.5cm'.

I'm pretty sure they're the same thing, except I think "accuracy" may be used a little more often.

Precision refers to the repeatability of measurement. It does not require us to know the correct or true value but Accuracy refers to the agreement between a measurement and the true or correct value.

I agree with Claire. Pi is 3.142, accurate to 3 decimal places but to be more precise it is 3.141592654.