@otswe
Actually If Im not wrong, you CAN host a website on a different dedicated server than your actual server. Why people do that? For a very simple reason. When there are DDoS attacks on their server which they have website on, the game itself is not affected - it also works vice versa. In case you have both things on the same server, and you get DDoS, both your server and website will be affected by that.
But of course when you start and you don't have much money, you have both server and website just on one dedicated server. After some time if your project is successful and you think you can afford another dedicated or VPS server for your website for a safety reasons, you can do it.