Phylogenetic Systematics focuses on identifying unique (derived) shared characteristics, called, synapomorphies. These are distinguished from primitive shared characteristics, which are called plesiomorphies. Only synapomorphies can provide information about the evolutionary history of a group; its phylogeny. The aim is to identify what Hennig called monophyletic groups, that is groups consisting of common ancestor and all its desendents. These are known as clades. This is represented in the form of the now familiar and ubiquitous tree like diagram called a cladogram. In contrast to evolutionary systematics, Phylogenetic Systematics only acknowledges monophyletic groups. The relation between the different clades is shown by a tree-like diagram or cladogram. Because there are any number of possible alternative cladograms (or evolutionary histories), only the simplest one, requiring the least number of changes, is chosen.
In short, Linnaean taxonomy and Evolutionary Systematics are concerned with both plesiomorphies and synapomorphies, whereas Phylogenetic Systematics is only concerned with synapomorphies only; Evolutionary Systematics is concerned with both monophyletic (also called holophyletic) and paraphyletic groups (made up of a common ancestor and only some of its desendents) , whereas Phylogenetic Systematics only with monophyletic groups. And unlike Evolutionary Systematics it does not use a specific Linnaean hierarchy of ranks (e.g. class, phylum). This is why cladists woin't even recognise Class Reptilia as a natural group; because reptiles evolved into two other taxa, birds and mammals, they are paraphyletic rather than monophyletic. MAK130320
In this context, the following definitions are used