Macs can read and write to “PC” MS_DOS FAT and ExFAT formatted drives
natively.
Macs can only read (not write) to NTFS drives without 3rd-paty software.
And of course they can read-rite to Mac-formated drives (Mac OS Extended)
So if your drive is NTFS, you will need to buy software to write to NTFS
drives (google it) or get a Mac drive and copy everything to it.
And of course your permissions for the files on the drive must allow you
to write, but generally on local drives (as opposed to NAS or other
networked drives)
Photoshop has it’s own additional issues (Apple bug) that prevents saving
while a file is being previewed in the Finder (“file explorer”)
SO I always click away from the file I am working on so that it’s preview
is now displayed in the Finder wndow - then I can save.