How old / what vintage for the wheel and the cassette? Was the wheel (freehub reallydescribed as 10 speed ? Or 10/11 speed ?

When 10 speed was introduced by Shimano, the freehub of course suited 10 speed. Buy.then came 11. Sensibly for once, wheel (hub) manufacturers made them suit 10 and 11 speed. It had a spacer at the back for when on 10 speed.
I recall (happy for someone to.chime in and correct this if not quite right) some early 10 speed cassette bodies were a tad thicker too.

Not sure how to explain why your two different cassettes required different spacers, but if it’s an 11 speed free hub then it is supposed to have two spacers for a 10 speed cassette: one 1.85mm spacer and one 1mm spacer.

Critical info needed: what kind of wheel is your Hed? 8/9/10-speed freehub body, or 11-speed freehub body?

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It’s the 11 Speed free hub

Bingo. That wheel and freehub is not compatible with a 10 speed cassette without the addition of a dedicated spacer.

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I’m aware that a spacer is needed.

What’s confusing me is that my new ultegra cassette needed two spacers where my previous cassettes (shimano and SRAM) only needed one spacer.

All on the same hed wheel?

Can you post an image of the single spacer you used with your previous shimano 10s cassette?

Can you also post an image of the two spacers you need to use with your new shimano 10s cassette?

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As already mentioned, there are different freehub bodies. Sometimes there is (or was) a spoke protector. Regardless, you need to use spacers so the gears are tight and the first smallest cog is properly positioned from the end of the axle -

10 speed shimano is 1 mm narrower than 10 speed SRAM.

You always need a 1 mm spacer on a standard hg shimano type freehub with a shimano casette but no spacer from SRAM.

You'll need 1.85 mm and 1 mm spacer for shimano 10 speed on 11 speed freehub but just 1.85 mm spacer for 10 speed SRAM on 11 speed freehub.

There are some obscure tiagra level cassettes that have the 1 mm spacer built in. MTb cassettes as well are slightly different.

Reason for the SRAM/ shimano 10 speed difference is that shimano introduced an aluminum freehub body design with higher flanges n their higher end hubs to prevent gouging and save weight, and only shimano cassettes are compatible with both hg-type and new 10 speed. The design was dropped after a few years.