Accuracy, precision, and the words metrology keeps getting wrong
The two are not synonyms, and treating them as one is how a measurement process passes calibration while producing consistently wrong parts.
Accuracy is how close a measurement sits to the true value. Precision is how close repeated measurements sit to each other. A gauge can be excellent at one and poor at the other, and the failure modes look completely different on a shop floor.
A precise but inaccurate instrument is the more dangerous of the two. It produces tight, confident, repeatable numbers that are all wrong by the same amount. Nothing in the readings looks suspicious. Every part measures the same, so the process appears to be in control right up until an assembly fails or a customer gauge disagrees.
Resolution is a third thing entirely
Resolution is the smallest increment an instrument can display. It is not accuracy and it is not precision, and a display with more digits does not mean the extra digits carry information. An indicator reading to a tenth is not automatically trustworthy to a tenth.
The related trap is significant figures. Recording every digit the screen offers implies a confidence the measurement chain may not support, and those extra digits then get treated as real by whoever reads the record later.
Why the distinction earns its keep
Calibration corrects accuracy. It compares the instrument against a traceable standard and establishes the offset. It does not improve precision, because scatter comes from the instrument, the fixture, the environment and the operator, not from the reference.
So when a measurement process is producing bad parts, the first question worth asking is which of the two failed. If readings scatter, look at the fixturing, the technique and the temperature. If readings agree with each other but not with the customer, look at the calibration and the reference.