ΔE 15.3, loose: different enough that you should pick on purpose. Leather Brown is a little lighter, more saturated, warmer than Rust.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Leather Brown is a little lighter, more saturated, warmer than Rust.
The same difference applies the other way round: Rust is a little 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 Rust on the colour wheel See Leather Brown on the colour wheel
All matches: Rust equivalents · Leather Brown equivalents