XGBRegressor score (R2) vs. eval_metric (RMSE) According to the API Reference, XGBRegressor().score() returns R2.
However, according to the XGBoost Paramters page, the default eval_metric for regression is RMSE.
In my understanding, scoring and using an evaluation metric is the same. So what am I missing here? Does XGBoost use different defaults for its native API and the Scikit-Learn API? Or do these two options mean something different?
Thanks a lot!

This is a bit strange, but $R^2$ and $RMSE$ are just functions of each other, so they are, in some sense, conveying the same information.
$$
R^2=1-\dfrac{
n\big(RMSE\big)^2
}{
\sum_{i=1}^n\big(
y_i-\bar y
\big)^2
}
$$
Some people see $R^2$ as easier to interpret. I disagree with the idea that we can liken $R^2$ to grades in school where $0.9$ is an $\text{A}$ that makes us happy and $0.5$ is an $\text{F}$ that makes us sad. Depending on the context, $R^2=0.5$ might be considered spectacular, while another situation might mean that $R^2=0.9$ is rather pedestrian performance.
