moving photos library to a other drive

Assuming it's a Managed Library (see below), then be sure the drive is formatted Mac OS X Extended, Journaled or apfs, and then drag and drop.

If you're running a referenced library (se below) then fist consolidate the originals into the library and then do the same.

A Managed Library, is the default setting, and Photos copies files into the Photos  Library when Importing. The files are then stored within the Library package

A Referenced Library is when Photos is NOT copying the files into the Photos Library when importing because you made a change at Photo -> Preferences -> General. (You unchecked the option to copy files into the Library on import) The files are then stored where ever you put them and not in the Library package. In this scenario you are responsible for the File Management.

"Managed Library" is the default, and it would be most unusual for your Library to be Referenced, but accidents happen.

As Yer_Man says, the new Drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. The drive must be connected directly to the Mac by cable, not networked, clouded, NASed, etc. You can see this:

Move your Photos library to save space on your Mac - Apple Support

If you double click on a Library, then that's the one that opens, and that's the one that will open the next time you run Photos.

If you are using iCloud Photos, only the System Library connects to iCloud, and it shouldn't be switched around willy-nilly.