Accuracy and precision depend on many factors, including the device and the clarity of the signal received. I'm answering based on the assumption that the device used is not supported by additional signalling equipment on the ground (with known locations).
The signal from the GPS satellites is cleaner if it arrives directly at the device without interference from (degregation due to / reflection from) trees, buildings, mountains, cliffs, etc.
A device may be better or worse at dealing with such interference. A device may be better or worse at calculating a position based on conflicting signals from one or more of the satellites (the device can't necessarily tell which are clean signals and which have suffered as above).
A device may be better or worse at improving the accuracy of the recording of a single point by being left stationary over some time. Some devices can be told that they are stationary (so being able to gather information over time about a single point). Others can't (therefore interpreting changes in signal as movement not additional information)
It's presumably possible, at least theoretically, that a device which is more accurate than others in one scenario might not maintain that increased accuracy (or precision) in other circumstances.
In practical terms, typically on consumer-grade GPS equipment the equipment's calculated location varies, perhaps considerably, each time it calculates. I've come across devices which have been good at precision (noticing a movement of 5 metres despite an overall error of 30 metres - under tree cover) but with no consistency to this. Walking away from the location to an area with clearer signal then returning to the measurement site offsetting the original location by 30 metres.
The more practical extension of your question is probably going to be more like one of the following:
- "how accurate, and how precise, is this specific piece of equipment, in this specific set of circumstances?"; or
- "how accurate/precise is it possible to be with a consumer grade/full professional device / full professional setup including ground stations, in this specific set of circumstances?".
See also: What is the practical limit for lat/long measurement accuracy?