Tk and Tkx are different implementations. Tkx appears to have support for Aqua and/or X11 while Tk requires X11 (see this thread: building Tk without X11 on mac OS).

If you are not using a packager and intend to deploy your script simply by providing a copy of the script, the end users will need to have Xquartz and all required perl modules installed. If you wish to give your users a stand-alone executable, you could try to package up your app using PAR::Packer. This thread (Perl/Tk and PAR::Packer on OS X) has a discussion on trying to create a stand-alone executable of a Perl/Tk app; however, the conclusion seems to be that the end users of the executable would still need to have Xquartz installed.