To be accurate means to be correct or free from error, as in an accurate diagnosis.
Another meaning of “accurate” is conforming to truth or a standard, as in an accurate gauge.
To be precise means to be minutely exact, down to a couple of decimal points, as in “just at that precise moment.”
Precision also refers to conformance to a strict standard, pattern or convention, which is why it is sometimes confused with accuracy. Think of it as a very narrow range of tolerance.
To illustrate the difference, let’s consider the length of a piece of pipe.
“This is a three-foot piece of pipe” may be an accurate statement. Think “correct.”
“This pipe is 3.05 ft long” is a precise statement. Think “exact.”
Now, do you think you have an accurate understanding of the difference between “accuracy” and “precision”?