That's the purpose of the ability to extend a web application in SharePoint (associated with Alternate Accessing Mapping)
You create your first web application, your intranet, assign it to a dedicated content database and do whatever you need to do. Later on you will extend the web application to another url. Both will point to the same content database but can have different authentication mechanism (I guess you won't ask people on the internet to connect through NTML if you were using that in your Intranet)
Please keep in mind the authentication mechanism, and the location of your server, usually intranet content / access will be located within your corporate network while a public (internet) site will be located outside (in your DMZ). How will the internet user reach your environment ? How will they authenticate themselve, etc.