Let me try to explain: Swapped wheels last year with a friend...his (Ksysirum 10 spd), mine (Helium 9spd...both Shimano) Put the 9 on the Ksy., and put the helium and his 10 spd setup to rest in the shop...in pieces.
.When I took apart the 9, and put it on the new wheel (that the 10 was on), it was sloppy. I noticed a thin ring on the 10...after the largest cog...I put that on the 9 (on the new wheel) and it fit nice.
NOW...I have to return his wheelset...went to do the swap and found that I have another thin ring that showed up... I can't figure out one was on the 9 and one on the 10...were both on the 10???? But, the 9, put back on the old wheel fits nice (no ring). The 10, back on the new wheel fits OK with one ring. BUT...where does this one ring go. Do ALL cassettes have this thin ring and it goes on the 9spd? Do the 10spd have TWO thin rings?

Let me try to explain: Swapped wheels last year with a friend...his (Ksysirum 10 spd), mine (Helium 9spd...both Shimano) Put the 9 on the Ksy., and put the helium and his 10 spd setup to rest in the shop...in pieces.
.When I took apart the 9, and put it on the new wheel (that the 10 was on), it was sloppy. I noticed a thin ring on the 10...after the largest cog...I put that on the 9 (on the new wheel) and it fit nice.
NOW...I have to return his wheelset...went to do the swap and found that I have another thin ring that showed up... I can't figure out one was on the 9 and one on the 10...were both on the 10???? But, the 9, put back on the old wheel fits nice (no ring). The 10, back on the new wheel fits OK with one ring. BUT...where does this one ring go. Do ALL cassettes have this thin ring and it goes on the 9spd? Do the 10spd have TWO thin rings?
The thin spacer goes with the 10-speed cassette. The 10-speed is slightly more narrow than the 9-speed cassette.

For the thicker one - Mavic made (makes) a 10-speed cassette that was compatible with Campy 10-speed but fit on Shimano-type splines. It was wider than a Shimano-9 so a Shimano-9 required a spacer to fit. Problem is that I don't know which of your Mavic wheels was built this way - either? both?

You should be able to tell. If it was made to take the Campy-10, the Shimano-10 will require both spacers.

TF

The thin spacer goes with the 10-speed cassette. The 10-speed is slightly more narrow than the 9-speed cassette.

For the thicker one - Mavic made (makes) a 10-speed cassette that was compatible with Campy 10-speed but fit on Shimano-type splines. It was wider than a Shimano-9 so a Shimano-9 required a spacer to fit. Problem is that I don't know which of your Mavic wheels was built this way - either? both?

You should be able to tell. If it was made to take the Campy-10, the Shimano-10 will require both spacers.

TF
So, I'll assume that my old Heliums take NO spacers... That the two spacers were both from the Ksy's 10spd. I mean, they came from somewhere!