I'm installing 4.10's in a diff. that had 5.13's with a spacer.
I first installed the carrier without changing side shims and
have way to much backlash. Is there a thin and thick 4.10 ring?
What does the series (2,3 or 4) refer to??

Richmond makes "thin" 4.10 Dana 60 gears that must be used with a ring gear spacer or a 5 series carrier.

All other brands of 4.10 gears will work with your 3 series carrier.

Thanks Dr. Diff, I think you nailed it. It is a Richmond gear 6900521.
Since I already have this set, and the pinion installed, I can use
the ring, but with a spacer? Not a problem, this car will be for street use only. I wonder if Richmond make a thicker
4.10 ring?

Yes, you must use the spacer.

Richmond does not make a standard thickness 4.10 ring and pinion.