One file.
Different screens.

A calibrated display and an agreed viewing environment give you a stable place to judge the image. They help separate a grading decision from a display or playback difference.

Calibration does not make every consumer screen identical. It provides a known reference for the decisions made in the grade.

The image’s pixel values and its color metadata do different jobs. Primaries, transfer characteristics, and matrix coefficients describe how a player should interpret the signal.

A transform changes the image values. A metadata tag describes those values. Changing a tag alone does not perform the corresponding image transform, and different applications may handle the information differently.

Check the intended delivery space, the project’s output transform, export settings, file metadata, player interpretation, operating-system display management, and the display itself.

Compare the same export through a known monitoring path before changing the creative grade. Otherwise it is easy to compensate for one player and create a new problem elsewhere.

Agree the viewing conditions and required delivery specification with the client or distributor. Make a small test export early, verify it, and keep the approved master clearly identified.

My longer Hungarian article walks through these relationships. Its older version-specific menu examples should be read in that historical context.