No difference, really. TUDCA is UDCA with a taurine amino acid attached to the UDCA molecule. Hence the name Tauroursodeoxycholic acid. It simply converts to UDCA when in your body.
There have been claims made that TUDCA is 'superior' to UDCA in bioavailability to the body, but this has never been proven in any studies or anything. In the end, they're the same damn thing.