In a bivariate case where there  is one response and one predictor the square of the Pearson correlation and the coefficient of determination is the same thing. When there is more than one predictor being analyzed simultaneously,  you can only use the coefficient of determination. One rather informative way that it can be calculated is as the square of the correlation between the observed values and the predicted values of a regression model.

Are you sure this is the correct method for you - you may like to read the most cited paper I know of

Statistical methods for assessing agreement between two methods of clinical measurement JM Bland, DG Altman,  The Lancet 327 (8476), 307-310

https://en.wikipedia.org/wiki/Bland%E2%80%93Altman_plot

has this comment:

 "Bland–Altman plot (Difference plot) in analytical chemistry and biostatistics is a method of data plotting used in analyzing the agreement between two different assays...............Bland and Altman make the point that any two methods that are designed to measure the same parameter (or property) should have good correlation when a set of samples are chosen such that the property to be determined varies considerably. A high correlation for any two methods designed to measure the same property could thus in itself just be a sign that one has chosen a widespread sample. A high correlation does not automatically imply that there is good agreement between the two methods".

I assume you are undertaking a bi variate analysis? If so what Kelvyn outlines above is correct (they are the same, however they explain different aspects of findings.

The meaning of r and R2 as a measure of the quantity of the association is different (both meanings being valid) but these coefficients in no way contradict each other and both are the same whether you predict Y~X or X~Y.

For two quantitative variables X and Y, for which n pairs of measurements (xi, yi) are available, Pearson’s correlation coefficient (r) gives a measure of the linear association between X and Y.

It is often difficult to interpret r without some familiarity with the expected values of r.

A more appropriate measure to use when interest lies in the dependence of Y on X, is the Coefficient of Determination, R2. It measures the proportion of variation in Y that is explained by X, and is often expressed as a percentage.

r is useful as an initial exploratory tool when several variables are being considered. The sign of r gives the direction of the association.

R2 is useful in regression studies to check how much of the variability in the key response can be explained. it is most valuable when there is more than one explanatory variable. High values of R2 are particularly useful when using the model for predictions.

R2 is only a descriptive measure to give a quick assessment of the model. Other methods exist for assessing the goodness of fit of the model. Adding explanatory variables to the model always increases R2, therefore in practice, it is more usual to look at the adjusted R2, adjusted R2 is calculated as 1 – (Residual M.S./Total M.S.)

As with R2 , the adjusted R2 is often expressed as a percentage.

Although both parameters have been used through time, you should really only use R2 if you want to find the amount of variance in Y that is explained by your model:

R2=1 or 100% - Perfect fit; your model explains 100% of the variation of Y over your independent variable X or variables (X1, X2, etc.)

R2=0,5 or 50% - Your model equation is only able to explain 50% of the observed Y values over X (or X1, X2, etc.)

R2= 0 or 0% - no correlation between independent and dependent variables

What is a "good" or "not so good" (or even "bad") model depends very much on the area you are working, because if in physical chemistry, in most instances, you easily reject a model with, say, R2=0,8 or even 0,9, in medicinal chemistry or in social sciences this would probably be a "very good" model, since data has usually more uncertainty and systems are more complex.