RC works by injecting the JavaScript functions into the browser for testing. This is a slow process because it involves a RC(Remote Control) server and RC Core to perform testing. RC core injects the javascript code on the RC server because RC Core cannot straight away perform testing on a web page hosted on another domain thanks to the same origin policy. To learn more about the same origin policy or about the drawbacks of RC, read this blog:
https://www.edureka.co/blog/selenium-tutorial.
WebDriver was the flavor of Selenium which overcame a lot of challenges faced by RC. To comply to the same origin policy, and at the same to perform the required tests, WebDriver uses a proxy server to inject the selenium code on the browser. This what we mean by "Selenium-WebDriver makes direct calls to the browser using each browser’s native support for automation".
So on a concluding note, WebDriver is just a better & faster version of the now outdated Selenium RC.