Yes, measurement error and measurement uncertainty are two different concepts but many laboratory personnel somehow cannot really differentiate them. It is utmost important for them to see their differences.
We know all measurements are affected by uncontrollable factors. No two replicated measurements give exactly the same result, except physical counting of objects.
By definition. error is the difference between an individual test result and the true value of the measurand (targeted analyte) in a given sample, whilst a true value refers to the actual amount of the measurand present in the sample. In fact, all true values by nature are indeterminate, meaning that they can only be determined under perfect analysis conditions which are not achievable in practice.
If we were to use a certified reference material for our laboratory analysis, then an observed measurement error would then be the difference between the observed value and its reference or certified value which by itself carries an uncertainty as well. These values are not 100% true values!
When we find a measurement error is systematic, i.e. the measurement results differ significantly from the reference or certified value, we say the mean measurement result has a bias and such systematic error may be corrected with a correction factor, if deemed necessary. Even after the correction, the reported value still has a certain amount of error.
Measurement uncertainty, on the other hand, is expressed in the form of a range or interval after evaluating all contributions of uncertainty factors, and, if estimated for an analytical method and defined sample type, may apply to all determinations so described.
The measurement uncertainty therefore tells us what size the measurement error might be, and the range would have covered the true value at a certain level of confidence, such as 95%. In general, the value of the uncertainty cannot be used to correct a measurement result.
It is important to stress that the uncertainty of the result of a measurement should never be interpreted as representing the error itself, nor the error remaining after correction.
The following sketch gives a clear picture of the differences between measurement error and measurement uncertainty.