ΔE 23.5, loose: different enough that you should pick on purpose. Hydra Turquoise is noticeably darker, much more saturated than Bright Gun Metal.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Hydra Turquoise is noticeably darker, much more saturated than Bright Gun Metal.
The same difference applies the other way round: Bright Gun Metal is noticeably lighter, 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.
See Bright Gun Metal on the colour wheel See Hydra Turquoise on the colour wheel
All matches: Bright Gun Metal equivalents · Hydra Turquoise equivalents