The key difference is in how they manipulate and work with your site files. I've emphasized files because, in order for any web-page to exist, it must have a file, on a server, somewhere, and that file must contain standardized HTML code. Many hosts bundle and "blur" the lines between these distinct pieces for simplicity; however, all web-sites consist of the aforementioned parts.
A Site Building program - like SiteBuilder - is truly that. You tell it how you want the site to look, and it builds it. While it does store a history of your previous editions to the site so that you can further modify it, it does not "edit" the site files in any sense of the word. Instead, it stores everything you tell it (about how your site is structured) in a proprietary database, and when you're ready to publish, it takes that data, runs it through a script, then the script outputs a set of HTML files and images, and uploads them to the server. When you go back to make editions to the site, it does not go back to the server and retrieve what it published previously - instead, it goes into its database, and retrieves the most recent list of updates you made to the site, so you can pick up there. You can see, with a "builder" it is not editing files, rather it is creating new ones each time you publish the site. This means that, if you edit a file outside of the builder after you've published it, the builder will not take those changes into account as it does not know they exist, and will overwrite them when you re-publish. Additionally, this means that in order to move your site to another host, and pick up where you left off, you would need the new host to have the exact same builder software, and your old host would need to provide the backup of your site in the proprietary format that the builder uses, so that the new host can have the files restored exactly as they were before. This is the primary reason that professionally built web-sites are not made on builder programs.
A site editor or WYSYWIG editor literally edits the pages. When you open up the page, it connects to the server, downloads the current version of the file, parses it (like a web-browser would) and shows you what the page will look like. When you make an edit in the code manually, it shows you how the page looks after the edit. Additionally, when you make an edition through the simplified interface, it updates the code for you. Since it is literally "reading" the code, then changing it, and finally re-writing it to the server, any changes made will not be recognized by builder programs.
Site Building Software is basically used for clients to create their own website, while a site editor can be used to modify a site designed by a professional.