When choosing a risk metric, an agent is picking an aspect of perceived risk to investigate, such as volatility or probability of default.
[1] In a general sense, a measure is a procedure for quantifying something.
[2] In other words, the method or formula to calculate a risk metric is called a risk measure.
For example, in finance, the volatility of a stock might be calculated in any one of the three following ways: These are three distinct risk measures.
Each could be used to measure the single risk metric volatility.