It is important to point out that this is an approximation since the true relationship is influenced by further factors such as temperature and humidity. But incorporating all this would be close to overengineering (at least for calculating a climb rate which is what varios will do and will be most important for pilots) which is why there is a standardized approximation given by the ICAO Atmosphere. The ICAO Standard Atmosphere for instance assumes a temperature of 15 °C and a pressure of 1013.25 hPa at mean sea level and a lapse rate of 0.65 °C per 100m. Maybe one of the key points of the barometric formula is that for calculating the (correct) mean sea level altitude the right reference pressure needs to be used. The pressure level at sea level must be known, which leads to QNH a virtual reference pressure at mean sea level that can be retrieved from METAR information of airports in the vicinity.
Accuracy means: Measured value is close to the true value to be measured. An accurate barometer would report close to 1013.25hpa if the true pressure would be equal to 1013.25 hPa. Except for the calculation of flight levels the relevance of an accurate barometer is not crucial from a practical point of view. After all a lack of accuracy is equal to an offset in the reported value and can be fixed with adding a constant value or resetting the reference value to a new, a correcting value. Practically this is already being done when you start working with QNH, QFE or Mean Sea Level adjustments based on the GNSS. So apart from maybe Flight Levels (FL) which are always based on the same reference pressure, 100% accuracy is not as relevant as maybe thought.
Precision describes the range of deviations when measuring continuously the same value. The bigger this range, the less capable is the sensor to detect small changes in pressure. Why is that? Well if this range would be 50cm wide, the barometer is practically not capable to detect a 20cm change since it is well within its own range of measurement uncertainty. At least not based on a single reading. With that, for the calculation of a climb rate, more interesting than the accuracy of a barometer is the following question:
And connected to that a question that leads directly to sampling rates and precision:
Try finding that out for your recently bought vario :-) .
Or more specific. If paragliding pilots point out that only their high end vario is capable of detecting a change in altitude of 10 cm or maybe even 5 cm. And this is what supposedly helps them to thermal. What does that actually mean?
A vario and especially the used barometer can be way off in terms of accuracy yet be extremely precise. This is not problematic since that offset can be compensated. If you know something is of by 10 meters, well take these 10 meters off! Of course, the other way is also possible. A barometer can be accurate but not precise, which would be much worse. This would be problematic since their is no other compensation than increasing the integration time and with that the climb rate of that vario would get more and more delayed. If a vario is not precise it will need to take a lot more samples to calculate more precise values by averaging