All rings of power, save the one, were forged with the intent that they should help that wielder govern their race and realm. So there was little difference between the 7 and 9. The 7 and 9 rings were intended for dwarves and men, yes. Sauron had a hand in the forging of the great rings and touched all but the 3. (which is why the three are not corrupted.) All of the 7 were lost over time, and the nine, as we know, turned the kings that bore them into ringwraiths.
***A.B.B.A.***
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