ΔE 15.7, loose: different enough that you should pick on purpose. Charred Brown is noticeably darker, more muted than Burnt Offering.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Charred Brown is noticeably darker, more muted than Burnt Offering.
The same difference applies the other way round: Burnt Offering is noticeably lighter, 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 Offering on the colour wheel See Charred Brown on the colour wheel
All matches: Burnt Offering equivalents · Charred Brown equivalents