In statistics. science, and engineering, there is a difference, and it is not explained completely clearly by any other answer. My brother and I, in writing Business Statistics Demystified (McGraw-Hill, 2004) spent two weeks writing four pages to make this clear. That's longer than we spent on some other chapters!
What physics and engineering call precision, statisticians call reliability.
What physics and engineering call accuracy, statisticians call validity.
Imagine 4 archers each shooting 10 arrows at a target, aiming for the bulls-eye.
One of them shoots all 10 arrows very close to one another, in a two-inch circle. Unfortunately, all the arrows are about 2 feet away from the bulls-eye, say, to the left. This shooter is very precise - he does the same thing every time. But he is not very accurate. He has a bias of 2 feet to the left.
The second archer shoots all around the bulls eye - everything is in the yellow or blue, but none is in the red. Some are above the bulls-eye, others below. Some are to the right, others to the left. He is very precise - the center of all of his shooting is the center of the bulls-eye. But he is not precise enough. He needs to become more steady and reduce variability from the center.
The third archer sends all ten arrows low, to the bottom of the target, and scattered around. He is neither precise nor accurate. He needs to become more precise by eliminating his bias (too low) and also become more accurate.
The fourth archer lands all the arrows closely grouped in the bulls-eye, centered right at the center. He is both accurate and precise.
In physics and engineering, we know where the target is. In statistics, we can't see the target. That's why statisticians use a different term.