Correlation refers to a comparison between two items to quantify the differences.
Calibration refers to comparison of an item of greater known accuracy to an item of lesser unknown accuracy. The known accuracy being based on national or international standard values.
You could use calibrated instruments for a correlation. You could also use uncalibrated instruments.
Holding two ears of corn, one in each hand and correlating the lengths --- "Let's see now, this one looks a little shorter than the other one when I hold them next to each other.." (example of a very simple correlation).
However, that correlation could not be considered a calibration. To calibrate an ear of corn, you would need tolerance limits, and measurement standards of known accuracy.
Hope this explains it. Correlation can be a subset of calibration.