It's very tricky because the way to distinguish them is to call the other ones in the same larger group 'true Salamanders' which already indicates that there was some historical confusion around naming these.

The tree of life has been re-arranged many times already and as more genomes are sequenced we discover more and more non-obvious mistakes. For instance 'Comb jellyfish' have caused a major stir amongst evolutionary biologists.

It's interesting how we needed taxonomy to figure out that there is such a thing as a tree of life and the basis for genomics and then, once we had that we had to go back and do (multiple) fairly major revisions to fix stuff that turned out to be wrong. The interesting thing is that the overall picture is still subject to such major changes.