The fundamental difference between phylogenetics and cladistics is that phylogenetics is the study of evolution, whereas cladistics is evolution.
The fact that cladistics has emerged from phylogenetics is due to the problem that speech is fundamentally inconsistent so that there is no single consistent arrangement of words, but instead many consistent arrangements of words, just as there is no single perfection of biological organisms, but instead many perfections of biological organisms.
This problem means that if a person studying evolution falls into the belief that there indeed is a single (“true”) consistent arrangement of words about evolution, then this person actually falls into the same search for perfection as evolution itself is about, ie, begins to evolve in search for the (non-existing) single (“true”) consistent arrangement of words about evolution.
This trap does thus not lead to a single (“true”) consistent arrangement of words about evolution (as believed, or hoped), but instead to a continuous diversification of (“true”) consistent arrangements of words about evolution, just as the evolution of organisms continuously diversifies kinds of organisms. The search for an impossibility factually results in the opposite. And, suddenly, it reenters the situation that prevailed before Linné presented his system of classification. Rational thinking has passed the orthogonal wheel around.
Biological systematics thus ought to avoid the trap called “cladistics”. The fact that it is inconsistent (ie, actually a belief) means that it leads rationality into a vicious circle (see Henri Poincaret).