ΔE 31.6, loose: different enough that you should pick on purpose. Battle Mud Wash is noticeably lighter, much more muted, warmer than Military Shader.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 32). Battle Mud Wash is noticeably lighter, much more muted, warmer than Military Shader.
The same difference applies the other way round: Military Shader is noticeably darker, much more saturated, 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 Military Shader on the colour wheel See Battle Mud Wash on the colour wheel
All matches: Military Shader equivalents · Battle Mud Wash equivalents