When I simply "drag and drop" the folder it only copies it of course.
Drag and drop the Photos Library to the other internal drive. Then double-click it to open it in Photos and test it thoroughly. Once you are satisfied that it is working in the new location, delete it from the internal drive.
Moving a library can occasionally result in file errors, and it is safer not move the library instead of copying the library. You may end up with an unreadable version on the destination drive.
To use a Photos Library on a different drive, the drive needs to have the file system "MacOS Extended (Journaled)", otherwise you may not be able to use the library there.