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Correlation analysis is the relationship of two values. When two items are similar, they will have a high correlation. Should they differ, they will be much lower in variables.
These are synonymous terms, but you would use the latter to sound more erudite.
Correlation is when two things are related or have similar properties and they can exist independently. Causation means that one thing made the other thing happen.
If measurements are taken for two (or more) variable for a sample , then the correlation between the variables are the sample correlation. If the sample is representative then the sample correlation will be a good estimate of the true population correlation.
Evidence that there is no correlation.