What's the difference between taxonomic and phylogenetic classification?

Taxonomy = nomenclature and classification.

Taxonomic classification would be a redundancy, similar to the expression "hoggy pig" or "hairy fur."  You probably mean the difference between traditional (Darwinian) taxonomy and "phylogenetic" (cladistic) taxonomy or the difference between traditional (Darwinian) classification and "phylogenetic" (cladistic) classification.

The traditionalists or Darwinians will tell you that a useful classification would take into account both morphological disparity and branching order.  They will tell you that a truly phylogenetic classification (as opposed to a cladistic classification) consists of both components: morphological disparity and branching order.  For example, a traditionalist may classify all reptiles into a single taxon they call Reptilia and they will classify birds in Aves and mammals in Mammalia.

The cladists classify differently.  They will lump all organisms, regardless of the amount of morphological disparity into a single taxon that consists of a single ancestor and all of its descendants.  Since birds descended from a reptile (probably Longisquama although the cladistic religion currently regard the dinosaurian origin of birds as indisputable gospel truth), they insist that birds MUST be included within Reptilia. They also insist that the synapsid and therapsid reptiles be removed from Reptilia and classified with mammals in a redefinition of "Mammalia."  As one can see, the difference between traditional classification and cladistic classification can be quite drastic.  

In fact, these philosophical differences, and the cladist's intolerance of paraphyletic taxa, is the major source of new taxonomic proposals published during the last 2 decades and a half.

Ideally, none.

Taxonomy is the science of naming and classifying organisms. It is done by looking at shared characteristics, such as morphological characters, against the background of biological diversity. It also takes phylogenetic relationships and DNA evidence into account.
A phylogeny is the evolutionary history of a species or group of species. They separate organisms by evolutionary relationships (clades), based on comparative cytology and the comparison of DNA, morphological characters, and shared ancestral and derived characters.


Read more: http://wiki.answers.com/Q/Difference_between_taxonomy_and_phylogeny#ixzz1a400sqU5