Both Lightroom Classic and ACR treat raws as read only. When you edit (parametrically) JPEGs, TIFFs PSDs etc, the edits are saved in the documents themselves but all this is done automatically, you don't have to do anything per se. DNGs can be raw data (as raw as the proprietary raws) and the instructions can also be saved in that container. Again, Adobe treats proprietary raws as read only hence, in ACR, there are sidecar files. You can bounce back and forth between ACR and LR if on version parity. Same engine, the edits are understood by both. With parametric edits, raws or existing rendered images like a JPEG, at some point, the instructions have to be rendered into a new iteration, this is where
Export (or
Edit in Photoshop for LR) comes into play. If you applied instructions to a JPEG in either, then just opened that JPEG in Photoshop, you'd see no edits. But they do exist. It is necessary for those edits to be rendered from the original JPEG to again, a new iteration which you could save as another JPEG or something else.
In
Export, you can set up as many parameters for the rendering as you wish: full size, resampled up or down, bit depth, color space etc. So one raw could end up as a JPEG at 1000x1000 pixels or a TIFF at the full resolution of the raw, in two different bit depths and color spaces.
Outside of all the Adobe tutorials, this is also a great site to examine:
https://www.lightroomqueen.com