Measure vs. metric

A measure is a general term - the result of a measurement action. A metric is a specific, standard measure used to make a judgement about capability or some other value, often in a technical or management context (e.g. 'mean time between failures' as mentioned by deadrat). An example of a metric in a specific context is a 'key performance indicator (KPI)' used in IT Service Management such as 'number of incidents per annum caused by changes'.

If you write for a technical public (especially mathematicians), prefer "measure", "score" or "indicator" unless you really mean to refer to a metrical space.

Strictly speaking, a measure or distance qualifies for being metrical when it satisfies three conditions [d(a,a) = 0; d(a,b) = d(b,a); and d(a,c) ≤ d(a,b)+d(b,c)].