With the print adjustments in the Print section you are more or less changing what the printer does when the same numerical RGB value is sent to the printer driver. Ideally the printer should be using an appropriate ICC profile so that neutral values in the Print section result in the printer output looking like the same image rendered on the computer's monitor. But if an appropriate profile is not available or not giving consistent results, then the print adjustments can be used to get in the ballpark. It probably won't be as accurate as a proper profile, but it might be good enough.

With soft proofing, you are limiting the possible RGB values displayed on your monitor by the viewing application to those which the printer, when already properly profiled, is capable of reproducing. That is, you are translating all of the RGB values in the picture to those within the printer's color gamut before then sending those numbers to the monitor and ultimately the printer.

Soft proofing is built upon the premise that the printer is already properly profiled. If the adjustments in the Print section are altered after the printer has been profiled, then the profile will no longer be accurate. (Note that the use of different papers with the same printer require different profiles for each type of paper.)