Those don't require any real changes to the bitmap data. In fact, those dimensions don't really exist in the image data. They are mearly virtual units created on the fly for the human use using the image's actual size in pixels and the PPI specification. When you lock out Ps's resampling, it can change the number of pixels as doing that requires resampling.
With resampling turned off, you can change the PPI seting either directly or by setting a linear dimension that Ps then uses to create the new PPI value. This type of change makes absolutely no change to the image itself. It merely changes a few numbers in the file's header.
The inch, mm, ... values do not exist in the file itself. The image portion of the file is just pixels, and there is a PPI value stored in the file's metadata. This concept was invented long ago and far away with the TIFF format so that PageMaker, specifically, could use it when scaling a placed file, using the embedded PPI value instead of the application's default (72ppi at the time). The Ps formats (PSD and PSB) follow this lead. The inch, mm, cm, ... dimensions that you see are calculated on-the-fly by the application using the pixel sizes and the file's current PPI setting.
When resizing is turned off in the Image Size dialog in Ps, the only value you can actually change is the PPI. Changing the file's actual pixels requires resizing. For user convenience, Ps allows you to change the PPI either directly in the PPI field or in a linear dimension (inch, mm, cm, ...) field and Ps will calculate the needed PPI change for you. The linear dimension fields are just different "doors" into the PPI "room", they just add a layer of "translation" for your convenience.