What's the equivalent of Linux's updatedb command for the Mac?

It's locate.updatedb on Mac.

sudo /usr/libexec/locate.updatedb

For more information see the locate.updatedb man page.

You can do sudo ln -s /usr/libexec/locate.updatedb /usr/local/bin/updatedb to make the updatedb command available.

Personally, I just installed findutils (use MacPorts or Homebrew).

Then you have GNU locate and updatedb.

updatedb won't work without sudo.

Personally I prefer to have a per user locatedb though; if you sudo other users will know the names/locations of all your files.

I have a cron job to run:

updatedb --localpaths='/Users/grogs' --output='/Users/grogs/tmp/locatedb'

And in my .zshrc .bashrc/.bashprofile:

export LOCATE_PATH="~/tmp/locatedb"

If you run locate without first updating the database, you have a chance to see the OS's recommended way by its output.

WARNING: The locate database (/var/db/locate.database) does not exist.
To create the database, run the following command:

  sudo launchctl load -w /System/Library/LaunchDaemons/com.apple.locate.plist

Please be aware that the database can take some time to generate; once 
the database has been created, this message will no longer appear.