Metrics vs KPIs
A metric is any standard of measurement - number of incidents logged, average time to log incident, percentage incidents resolved within agreed service level etc.
A Key Performance Indicator (KPI) is a metric that you have chosen that will give an indication of your performance and can be used as a driver for improvement. In general it's prefered to just chose a few KPIs (say 3 or 4) to focus on.
The point is this: a metric is just a measurement. A KPI is an indicator (a metric) that you have chosen, and agreed with your partners (whether internal to IT or with customers), that will determine whether you are meeting your critical success factors (CSF).