When analyzing an experiment, it's sometimes useful to separately consider 'accuracy' and 'precision'. Accuracy is how well the (average) measured value agrees with the 'true' value, which may be determined by use of a standard, and your term 'error' may correspond to 'accuracy'. Precision refers to the spread of measured values, which may refer to your term 'uncertainty'. It's possible to have very precise and inaccurate measurements, poor precision and high accuracy, or some other combination. Loss of accuracy is sometimes called 'systematic error', while lack of precision is sometimes called 'random error'.
http://www.colorado.edu/geography/gcraft/notes/error/error_f.html
Also, there is uncertainty in the underlying object itself if stochastic processes are present. One way to think about this is that we have imprecise information about the object (or process).