Error

This has different meanings depending on the context. 

It can mean a mistake, but to scientists working with experimental data it relates to the amount of uncertainty about the data - how wide the range of values are within which the true value of the data lies. 

Eg if a scientist states that the temperature is 20 °C ± 0.5°C then the error is ±0.5°C. They are not saying that a mistake has been made they are saying that they know the value is somewhere between 1.9.5°C and 20.5°C.