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Not a native speaker; I think I understand your point, though I fail to see a distinction between these two words: if the output is a number to the nth decimal, but it is not "accurate" (ie. the numbers are actually wrong), can it still be said to be "precise" ?

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Precise means lots of fine-grained information; accurate means close to the truth. If the weather is 20° exactly and one thermometer reads 20.2° and another 20.562° the first can be described as more accurate and the latter as more precise. Hence the expression, “precisely wrong”.

Yes, here's the typical example used to explain the difference between the two: https://blog.forecast.it/hs-fs/hubfs/accuracy-precision.jpg

In terms of probability density: https://www.allsensors.com/images/engineering/figure-1.png

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