In practice, the distinction is not very clear-cut, Knoppix 7.6.1 may be viewed as something of a 32/64 hybrid. Running the 64-bit kernel with the right 32/64 libraries, you may be able to make quite a few 64-bits applications run, and arch reports x86_64, exactly the same as my live Debian 8.3.0. I could run that as a 64-bits guest in kvm, but I couldn't make VMware install the 64-bits version of Workstation 10. There might be a workaround for that, but I don't take the time to look for it, for I am able to use standard Debian 8.3.0 in about the same way I have used Knoppix, with poor man's installs and persistent store.