When you have edited at least one of the style features of an object, open the menu to the right of the Style Name
In the screenshot you see that the style of an object has been changed (look at the + sign before the name SB). Open the hamburger menu (red arrow) and choose Create New Style, give this a new name.
Existing styles can be managed in the Object Style Manager (Preferences menu).
At this moment you are using the Default Smartshape style for that shape button. Changing that shape to a shape button is irrelevant for the style itself. Each shape style in the Object Style Manager has automatically styles for 3 of the 4 InBuilt states: Normal, Rollover and Down (the 4th state, Visited, is not in the style, a bug IMO). When you change a shape to a button on a slide it uses the same style but added those InBuilt States.
To be able to create a new style, you need to edit the style. Try changing the stroke or the fill color for one or more of the InBuilt states and a + sign will appear before 'Default Smart Shape Style'. At that moment the option 'Create New Style' will become available.
Object styles are components of the used theme. If you switch to another theme, you'll see that the Default SmartShape style will change, as well for a normal shape as for a shape button.
BTW I branched this to a new thread, because it has no relation with the first question. Makes it easier for other users to find the thread.