If you only wanted to change the Directory to save your projects then you can do it while saving the projects
If you want to free your C:\ Drive then Uninstall Photoshop and Lightroom and then within AAM you can Change the Install Directory from Preference
Storage Drive ?? Photoshop. What Platform and OS are you running.
I use PC therefore Windows. When I thing about Application like Photoshop I know the are going to be files all over the place. Windows like everything installed on the Boot disk. I gave up the fight many years ago and let windows have it way when application are installed using an installer. However besides the application files you have user files and I break user files down into to categories. Windows User files like applications settings, preferences, cashes, etc and user Data Files, Images, text documents, PDF. Applications like Photoshop also have add-ons an need swap space as well. While all Windows default library reside on the C: drive you can add additional storage to you document, music, picture and video libraries the are not on the c: Most of my user data file are actually on external ESATA drives or USB3 drives. System files, Application Files, Paging, swapping and backup are on internal SSd and Fast Disk drive. Some of the folder that look like they are on C: are actually shortcut links to folders on other drives.