https://www.linkedin.com/pulse/covariance-vs-correlation-kumar-p

A good link.

Covariance is the 2-point correlation function, -. Correlation refers to any correlation function .

For a Gaussian distribution, only, any correlation function can be expressed exclusively in terms of the 1- and 2-point correlation functions.

So, no, in general, the two methods aren't equivalent.

https://stats.stackexchange.com/questions/18082/how-would-you-explain-the-difference-between-correlation-and-covariance

Key Differences Between Covariance and Correlation

The following points are noteworthy so far as the difference between covariance and correlation is concerned:

Conclusion

Both measures only linear relationship between two variables, i.e. when the correlation coefficient is zero, covariance is also zero. Further, the two measures are unaffected by the change in location.

Correlation is a special case of covariance which can be obtained when the data is standardized. Now, when it comes to making a choice, which is a better measure of the relationship between two variables, correlation is preferred over covariance, because it remains unaffected by the change in location and scale, and can also be used to make a comparison between two pairs of variables.

From: https://www.linkedin.com/pulse/covariance-vs-correlation-kumar-p

No-it's the other way around: Covariance refers to the 2-point correlation function. The correlation of two variables, of course, is, by construction, their 2-point correlation function. However this is, also, their covariance, only if the data are Gaussian. Only in this case can the correlation of 4 variables be expressed exclusively in terms of the correlation of the covariance of the variables taken pairwise.

It's useful to be precise and not use ambiguous words.

There"s no such notion as ``standardized'' data-there is a notion of Gaussian data.

While for many people the only probability distribution they know about is the Gaussian distribution, data aren't, always, aware of that fact.

A measure used to represent how strongly two random variables are related known as correlation.

Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance. Correlation is dimensionless, i.e. it is a unit-free measure of the relationship between variables.

https://www.linkedin.com/pulse/covariance-vs-correlation-kumar-p

A good link.