yes those links are equivalent to the toolbar links in more recent skins (as Spike said), this article tells about the history of these changes, unfortunately the videos were made quite some time ago so they aren't showing more recent things.
You can change the slogan text from Administration > Site Settings.
I don't know what you mean by slogan text image, but if you want to use an image instead of text you can remove the <portal:SiteSogan control from layout.master and replace it with hard coded html that has an image.
Note that the slogan is not shown in many of the skins, it was something that Artisteer designs had so we implemented a control for it and we use it in the Artisteer skins.
Hope that helps,