ΔE 19.4, loose: different enough that you should pick on purpose. Hammered Copper is noticeably lighter than Light Gun Metal.
Can I use Hammered Copper instead of Light Gun Metal?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Hammered Copper is noticeably lighter than Light Gun Metal.
Can I use Light Gun Metal instead of Hammered Copper?
The same difference applies the other way round: Light Gun Metal is noticeably darker.
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.