Writing zeros to a disk is a good way to make it difficult to restore files from a disk. You definitely want to do this if you give away your disk.
The option all the way on the left isn't the one you want. It redoes the file system and marks all data as unused, but you can likely recover some of that data. Security option 2 does want you want, plus some random data for good measure. It would be very difficult to recover after that. Higher security options exist if you are paranoid.
Anecdote: I bought a Memory Stick from Gamestop about 15 years ago. It had been formatted, so no files were visible when viewing it on my computer. However, I was able to use Photorec to restore several MP3s and JPEGs. They definitely had not zeroed out the drive, or Photorec wouldn't have found anything.
If you don't think that zeroing out a disk is important for removing data, try this: Load a drive with photos, format it with no security in Disk Utility, then run PhotoRec. You will likely find most of the photos. Try again after using Disk Utility security options 2-4 and you won't find anything at all.
https://www.intego.com/mac-security-blog/how-to-securely-erase-data-from-your-mac-and-external-drives/
Erase and reformat a storage device in Disk Utility on Mac - Apple Support
https://www.cgsecurity.org/wiki/PhotoRec