The difference between Distance function and Metric
When used as nouns, distance function means a function used to calculate the distance between two points, whereas metric means a measure for something.
Metric is also verb with the meaning: to measure or analyse statistical data concerning the quality or effectiveness of a process.
Metric is also adjective with the meaning: of or relating to the metric system of measurement.
check bellow for the other definitions of Distance function and Metric
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Distance function as a noun (mathematics):
a function used to calculate the distance between two points
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Distance function as a noun (topology):
a metric
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Metric as an adjective:
Of or relating to the metric system of measurement.
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Metric as an adjective (music):
Of or relating to the meter of a piece of music.
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Metric as an adjective (mathematics, physics):
Of or relating to distance.
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Metric as a noun:
A measure for something; a means of deriving a quantitative measurement or approximation for otherwise qualitative phenomena (especially used in engineering).
Examples:
"What metric should be used for performance evaluation?"
"What are the most important metrics to track for your business?"
"It's the most important single metric that quantifies the predictive performance."
"How to measure marketing? Use these key metrics for measuring marketing effectiveness."
"There is a lack of standard metrics."
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Metric as a noun (mathematics):
A measurement of the "distance" between two points in some metric space: it is a real-valued function d(x,y) between points x and y satisfying the following properties: (1) "non-negativity": d(x,y) \ge 0 , (2) "identity of indiscernibles": d(x,y) = 0 \mbox{ iff } x=y , (2) "symmetry": d(x,y) = d(y,x) , and (3) "triangle inequality": d(x,y) \le d(x,z) + d(z,y) .
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Metric as a noun (mathematics):
A metric tensor.
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Metric as a noun:
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Metric as a verb (transitive, aerospace, systems engineering):
To measure or analyse statistical data concerning the quality or effectiveness of a process.
Examples:
"We need to metric the status of software documentation."
"We need to metric the verification of requirements."
"We need to metric the system failures."
"The project manager is metricking the closure of the action items."
"Customer satisfaction was metricked by the marketing department."