Hi Ian it's not that the engines are very different just was in between one company taking over another.The four Star was also know as a Model 7 and the four stroke was also known as a model 7a.
The four stroke run a LV22B Lauson four stroke and the four stroke run a LV30 Kirby-Lauson.
They were kind of nick named a four stroke Sheerline and they did have the same base.Not to sure why you think the bases are different as the only change was the extra ribs under the base.Also to pull the handles off was a little different.The four stars could be removed by pushing inwards and up.The four stroke you had to undo a scerw either side and then push in and up.Which was direct from the Sheerline.
You should (unless it's been changed) find two different carbys between them.
The four star has a Tecumseh carby (can't remember which model it was)and the four stroke run a Zenith carby model AH914-B2,I think.
You have the oval air filter,that is awesome I'd love to see some closer pictures of that.As most were replaced so they are getting harder to find.Mine doesn't have it on.
The four stroke had a spacer under the engine,my guess was just for looks as it didn't serve any other purpose than that.
You can see my two here,
My model 7 and 7a four stokesGizmo your one is in fact the model 7a,or four stroke.