Everything you do to a raw file is recorded as a set of instructions on how to interpret the original raw image data, which does not change (assuming the file doesn't suffer random data corruption in whatever storage medium it is held, or whenever it is copied to another storage medium) as long as the original file is retained.

Those instruction sets are generally proprietary to whatever application was used to create them. Work you do in Adobe products will not be applied if you later open the raw image file in other raw conversion applications, such as Capture One or DxO PhotoLab (formerly Dxo Optics Pro). Similarly, any work you do in Capture One will not be reflected when the raw image file is later opened using Adobe Camera Raw.

In the case of Adobe products, Adobe Camera Raw is used to interpret raw image files when worked with in other Adobe applications such as Adobe Photoshop or Adobe Lightroom. So whether you open the file in Adobe Camera Raw or in Adobe Photoshop, the raw conversion engine under the hood is the same: ACR. The interface is all that is different with regard to how raw files are handled in Photoshop. The additional functions/options of Photoshop that are not included in ACR are applied to the image information after it has been converted from raw image data to a raster image by ACR working in the background, and those instructions are also added to the file (or a sidecar file containing the instructions) without altering any of the original raw image data.

Changing the way an image looks on your screen using ACR, LR, or PS doesn't alter the original file at all until you "save" it. It just changes what you see on the screen by changing the way the raw image information is processed/interpreted. When you "save" your work, the instructions are added to either the image file itself or to a separate sidecar file associated with the image file. (There are options within ACR and all the other Adobe products that use ACR to interpret raw data that allows the end user to select whether the instruction set is appended to the main file or contained in a sidecar file.) In either case, none of the original image data is replaced. The instructions on how the original data is to be interpreted are added and used again the next time the file is opened using an Adobe product. If you "save" your changes, make additional changes and then "save" it again, the latest instruction set will overwrite the previous instructions with regard to the particular changes you made.

One analogy is that of a culinary dish. The raw image data is like the list of ingredients. The instruction set is like the various instructions on how to prepare those ingredients. One can take the same ingredients and prepare them differently and get two different results. One can even use only some (but not all) of the ingredients on the list to get various results. One might have one set of instructions for preparing the dish in a conventional oven, another set of instructions for preparing the dish using a microwave oven, and yet another set of instructions for using an open fire and a dutch oven. Changing the instructions on how to prepare them does not change the initial set of ingredients we start with. It does change, to one degree or another, what we end up eating.

However, a raw image file usually contains more information than just the image data collected from the sensor. Much of this information is stored in a portion of the file known as the EXIF information. Much of the EXIF info is standardized, but there are provisions for what are known as "maker notes" to also be included in the EXIF information. These "maker notes" allow each camera manufacturer to include whatever non-standardized information they desire in the EXIF info. For the most part, Adobe products ignore most of the maker notes section of the EXIF info, but other raw conversion applications, particularly those created by the camera manufacturer like Nikon's ViewNX or Canon's Digital Photo Professional, can and often do use some of that information when interpreting the raw image data.

When images are exported using Adobe products, much of the maker notes section included in the original raw file is not included in the EXIF info of the new file created by Adobe products. It's still there in the original raw image file unless the original is overwritten by the new exported file. Again, there are options from within Adobe's products to leave the original file and create another exported file or to replace the original file with the exported file.

For example, if one converts a Nikon .NEF file to .DNG using Adobe's convertor, the maker notes are stripped from the EXIF information and not included in the resulting DNG. If one only plans to ever use Adobe products this is no big deal, because all Adobe products ignore the information that is stripped. But if one later wants to use another raw conversion application that does use the maker notes info, that information is gone unless one still has the original .NEF as well as the .DNG made from it.