ΔE 19.4, loose: different enough that you should pick on purpose. Gun Metal is noticeably lighter, more muted than Burnt Iron.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Gun Metal is noticeably lighter, more muted than Burnt Iron.
The same difference applies the other way round: Burnt Iron is noticeably darker, more saturated.
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.
See Burnt Iron on the colour wheel See Gun Metal on the colour wheel
All matches: Burnt Iron equivalents · Gun Metal equivalents