Yes, there is a difference
In general use, the words accuracy and uncertainty describe how sure we are of something, but when used in measurement their distinct meanings are well defined and it is important - even vital - to use the correct word.
Accuracy of measurement is the older phrase and its internationally agreed definition is '… the closeness of the agreement between the result of a measurement and a true value of the thing being measured'. The definition adds: '... accuracy is a qualitative concept', so is often expressed as being high or low, but not with numbers.
In practice, though, it is often used quantitatively and the definition becomes '... the difference between a measured value and the true value'. This leads to phrases like '... accurate to ± X'. Unfortunately this unofficial definition breaks down because it inherently assumes that a true value can be defined, known and realised perfectly. Even in the finest national measurement laboratories, however, perfect values cannot be realised. It is simply impossible to define or make perfect measurements, neither nature or the laws of physics allow it.
Uncertainty of measurement acknowledges that no measurements can be perfect and is defined as a '… parameter, associated with the result of a measurement, that characterises the dispersion of values that could reasonably be attributed to the thing being measured'. It is typically expressed as a range of values in which the value is estimated to lie, within a given statistical confidence. It does not attempt to define or rely on one unique true value.
In summary, common usage of the word accuracy for quantitatively describing the characteristics of measuring instruments, is incompatible with its official meaning. But, even ignoring this point, its common usage definition is significantly cruder than the proper metrological term uncertainty.
Does the difference really matter?
In many situations the difference really doesn't matter at all and it remains much easier to say 'This instrument is accurate to…' rather than 'This instrument is uncertain by…'. Swapping convention might have been easier if the term was certainty and not uncertainty; but it isn't! And an accurate device sounds more impressive than an uncertain one too, which is probably why much equipment sales literature uses the word accuracy.
In recent years, however, great strides have been made in developing methods for quantifying the performance of measuring instrumentation, which can be relatively complex for even a simple instrument. If you are attempting to make a serious estimate of measuring performance, and persuade others that the result is valid, you will have to use the philosophy of uncertainty, and its adoption from the outset is thoroughly recommended.
For deeper explanations of these and associated concepts, download our free Beginner's guide to uncertainty in measurement