stars vs ranks 

I'd like to emphasize that your list is incorrect - ALL of the above are 3 star ranks, independent of how many stars they have in the insignia on their shoulders. 
Take a look at Major General - they are ALL 2 star ranks, but of the 40 insignia displayed on the page, 8 have no stars, 3 have one star and one has three stars. 
General officer#General ranks by country displays 26 insignia.
Admiral#Admiral insignia by country shows 16 insignia, of which only 5 have four stars.
If you want to continue your comparisons, you might find List of comparative military ranks useful. Also Air force officer ranks, Army officer ranks, Naval officer ranks, Ranks and insignia of NATO and perhaps United Kingdom and United States military ranks compared too. (One that interests me is that a 5 star French general's insignia contains 7 stars.)
Thanks for raising my interest! Cheers,