wilko185 wrote: I thought the 7 and 9 were conceived of as two distinct "sets", though it isn't clear in what ways they differed:
The problem here is that Tolkien’s writings are not clear on this matter. Every time except once he deals with the Sixteen as one group of Rings. Only in “Unfinished Tales” is there any distinction made.
A fuller quote from the text that wilko gave is
There Sauron took the Nine Rings and other lesser works of the Mírdain; but the Seven and the Three he could not find. Then Celebrimbor was put to torment, and Sauron learned from him where the Seven were bestowed. This Celebrimbor revealed, because neither the Seven nor the Nine did he value as he valued the Three; the Seven and the Nine were made with Sauron's aid, whereas the Three were made by Celebrimbor alone, with a different power and purpose.
Unfinished Tales: Concerning Galadriel and Celeborn
We have two choices here, one story-external and one story-internal.
The story-external explanation is that Tolkien is writing from a position where he (and the reader) already know that the Rings were divided into Seven and Nine. He is therefore explaining where these two groups of Rings came from.
However, it is always better to have a story-internal explanation, if possible, and I think there is one.
The quote clearly states that the Seven had already been “bestowed”, that is, were being worn by individuals, whereas the Nine were kept by the Mírdain themselves. This implies to me that there were two groups of Rings, and that the Seven had been made first.
However, Celebrimor clearly classed the powers of these two groups as similar, certainly when compared to the powers of the Three. Any differences between them must therefore have been small.
The idea that the Seven were created first fits, of course with the idea that the very first of the Seven was given by Celebrimor to Durin III. When one studies the likely politics of that time, from the hints given in UT, then I think this is quite likely and that Sauron in any case would have encouraged the offering of such a gift, binding the dwarves to the Celebrimor-Annatar power base and further isolating Galadriel from potential allies.
Once Celebrimor seized power in Eregion, the dwarves, who had been most friendly with Galadriel, offered her safe passage through Moria, but no other help.
As wilko pointed out though, this explanation seems to be contradicted by the passage in Of the Rings of Power and the Third Age which states that Sauron handed out all Seven.