A color space's primaries define which physical red, green, and blue it can produce
Two color spaces can share the same TRC but differ in which physical colors their R, G, B channels correspond to. A wider-gamut space has primaries further out on the chromaticity diagram, so its pure red is more saturated than sRGB’s. Identical numeric values (e.g. R=1.0) produce different on-screen colors across spaces with different primaries. Conversion between spaces with the same TRC (linear) requires a 3×3 linear matrix that maps one set of primaries to the other.
Examples
sRGB red primary: (x=0.64, y=0.33) on CIE xy diagram. DCI-P3 red primary is further out — P3’s 1.0,0,0 is more saturated than sRGB’s 1.0,0,0.
Assessment
Two displays show R=0.9, G=0.5, B=0.2 but the colors look different even after matching brightness. Name the likely cause, and explain what data is needed to convert between them.