Scripts, mostly JavaScripts, are rendered in order to speed up the loading times of websites. A distinction is made between prerendering, server-side rendering, and dynamic rendering. The terms are often used incorrectly synonymously, however. For this reason, Google recently uploaded a podcast that explains the subtle differences between the three types of rendering.
Prerendering applies to websites that undergo routine changes. This includes blogs, for example, because new content is uploaded regularly, which automatically changes the website.
On the other hand, for websites that make changes dynamically, such as social media websites, the technique used is server-side rendering. Dynamic means that the changes on these websites happen very frequently, so the HTML must always be recalculated.
Dynamic rendering is only a subtype of server-side rendering. JavaScript is executed directly on the server of the search engine, while the HTML is computed. JavaScript can be executed directly in the browser.
So the only thing that matters is the place where the script is executed. This can be on the side of the server or the clients.
