ΔE 23.2, loose: different enough that you should pick on purpose. Fire Opal is noticeably lighter, more saturated, warmer than Balthasar Gold.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Fire Opal is noticeably lighter, more saturated, warmer than Balthasar Gold.
The same difference applies the other way round: Balthasar Gold is noticeably darker, more muted, cooler.
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 Balthasar Gold on the colour wheel See Fire Opal on the colour wheel
All matches: Balthasar Gold equivalents · Fire Opal equivalents