ΔE 15.9, loose: different enough that you should pick on purpose. Ancient Copper is much more saturated than Moonstone Alchemy.
Can I use Ancient Copper instead of Moonstone Alchemy?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Ancient Copper is much more saturated than Moonstone Alchemy.
Can I use Moonstone Alchemy instead of Ancient Copper?
The same difference applies the other way round: Moonstone Alchemy is much more muted.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.