Will the 18" ten spoke Discovery 3 wheels (RRC 500251 XXX) fit my 2004 L322 and if so are the wheel nuts the same or will I need new ones?

Both wheels have the same PCD, Offset, Centre Bore Diameter and Mounting bolt size so it appears the answer to your question is, yes they will fit.
You would need the nuts to match with the wheels.

^^ there are 2 different sizes of wheel nut, the early L322 use a 20mm wide nut and the later ones use I believe 23.5mm. I am not sure as to the size that the Disco uses, but the wheel nut should be a snug fit in the hole in the wheel. All wheel nuts are the same thread for the L322 and D3/D4, best way of telling is to offer one of your nuts up and see if it's a loose fit , then try a wheel nut !
There should be no more than 0.5 mm of clearance, if your wheel nuts wobble around in the Disco wheel then you will need the bigger nuts
And likewise if your nuts are too big, cold water  Yesterday I couldn't spell Engineer... Today I are one!
Inventor of the 'Guide-o-Matic automatic wheel alignment tool'
Former long term L322 owner, Up/Down graded to a Classic Tractor!

Same nuts as the later-type FF on the D3/4 and RRS.  Visiting from DISCO3.CO.UK
Discovery 3 TDV6 Auto HSE Zambezi Silver

I have a set of disco 18" which o've got mud/snow tired on. Used them a couple of years ago on my l322 over winter with no problem. The over all diameter is a tad smaller so check your speedo, but should be fine. __________________
2015 FFRR SDV8
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2005 FFRR TDV6 - Gone

Size should be roughly the same 255 60 18 is the standard 18" disco size which is the same as the ones needed on the ffrr 18" wheels. There is nothing that can't be fixed with a hammer😜😜
FFRR 4.4 SDV8 Autobiography Santorini Black.
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2010 LR D4 Commercial 2.7 TDV6

255/60/18 is standard on the early ffrr, 255/55/19 is the later size, and I believe that 255/50/20 is the SC ffrr size. all have the same rolling diameter, give or take a fraction of a %. The only difference is the size of wheel nut, early had 20 mm diameter wheel nuts and the later ones have 23.mm diameter wheel nuts to bring them in line with the Disco's and Sport's, and moves them away from BMW sizes. Which is strange as they have kept the same size hub, so you can still fit Beamer wheels  Yesterday I couldn't spell Engineer... Today I are one!
Inventor of the 'Guide-o-Matic automatic wheel alignment tool'
Former long term L322 owner, Up/Down graded to a Classic Tractor!