Perceptual and output referred both transform non-linearly. Colorimetric and scene referred transform linearly.
There are two main color processing paths in photography. Perceptual and Colorimetric. 99% is Perceptual but it also distorts colors and tone in order to create pleasing images and also map large dynamic ranges in nature into either displayable or printable ranges. Colorimetric retains the exact color and tone, with the exception of white point transforms for differing illuminants. This is appropriate for reproduction purposes like taking a picture of a painting where you want to print a replica. But is completely wrong for normal photographs. And its not just dynamic range. Even when the output display or media are within the dynamic range, colorimetric processes typically produce unattractive images.
Most of the non-linear mapping of colors to produce pleasing prints is done by in camera or RAW processing tools and generates what is referred to as "output referred" images. A further, but much smaller, non-linear process transforms from the output referred image to output media. The latter accommodates a small (usually) dynamic range reduction in prints by scaling to the black point and increasing contrast in the midrange to produce a print that looks reasonably close to the output referred image on a monitor. This is what choosing "Perceptual Intent" during printing accomplishes. Alternately, one can accomplish the same but with more control by soft proofing using curves in Photoshop and printing using Colorimetric Intent.
For reproduction work you want to, if possible, precisely reproduce tone and colors. For instance if you want to make a duplicate of a comic book cover for marketing reasons you want to use colorimetric scene referred processing and either Relative of Absolute intent when printing. Absolute will retain the exact color of the reproduced art like the yellowing of an old cover. Relative intent will transform the white point which can be desirable in catalogs of new comics. For duplication, Relative intent can create somewhat darker images than the original since the white point is mapped to the print media so, for instance, a color with an L value of 80 might print with an L value of 76.
I find some or your terminology confusing. In an attempt to take the issue apart a bit, I offer the following:
Conversion of raw image values to an input-referred XYZ form (or any other linear RGB color space) using a compromise matrix is linear using most adaptation algorithms.
Conversion of raw image values to an input-referred XYZ form using a 3DLUT is in general nonlinear.
Conversion of raw image values to an input-referred sRGB form using either a compromise matrix or a 3DLUT is nonlinear.
Conversion of input-referred XYZ values to output-referred XYZ values is in general nonlinear.
Conversion of output-referred XYZ values to output-referred XYZ values in the presence of gamut limitations, using Absolute Colorimetric, is linear for in gamut colors, and nonlinear for out of gamut colors.
Conversion of output-referred XYZ values to output-referred XYZ values in the presence of gamut limitations, using Relative Colorimetric, is possibly linear for in gamut colors, and nonlinear for out of gamut colors.
Conversion of output-referred XYZ values to output-referred XYZ values in the presence of gamut limitations, using Perceptual, is likely nonlinear for in gamut colors, and nonlinear for out of gamut colors.
Conversion of output-referred XYZ values in the presence of gamut limitations to colorants of a particular printer is in general nonlinear.
I've used XYZ as a stand-in for any linear RGB color space in the above, and sRGB as a stand-in for any nonlinear RGB color space. Does that make sense to you?
Jim