Measurement error has historically been defined in the metrology community as a difference of 'values,' usually as a difference between a 'measured value' and a 'reference value.' The reference value is sometimes considered to be a 'true value,' which is unknowable, and so the 'measurement error' is then unknowable. However, in some cases the reference value is considered to be a value assigned to a measurement standard (e.g., a 'conventional value'), which can be known. In this case, 'measurement error' is regarded as being knowable and measurable (for example, the 'error of indication of a measuring system'). The characteristic of being "measurable" requires that there be a corresponding 'quantity' that can be measured. When measurement error is considered to be measurable, it must then be regarded as a 'quantity' (and not as a 'quantity value'). Although the concepts of 'quantity' and 'quantity value' are related, they are distinct concepts, and from a terminological perspective the same term ("error") cannot be used for both concepts. This paper addresses the dilemma of how best to regard 'measurement error' and associated concepts: as quantity values or as quantities. This distinction has important implications when considering the concept of 'uncertainty of error,' which arises when error is considered to be measurable.