Final answer:
Phenetic methods group organisms based on overall similarity without distinguishing homologous from analogous traits, while Cladistic methods focus on shared derived characteristics to establish evolutionary relationships and use cladograms to depict true evolutionary paths.
Step-by-step explanation:
The basic differences between Phenetic methods and Cladistic methods of determining phylogenetic relationships lie in how they classify organisms based on characteristics and evolutionary history. Phenetics, also known as numerical taxonomy, considers an organism's overall similarity, counting all observable traits equally, and often employs statistical analyses to group organisms. However, this approach does not distinguish between homologous and analogous traits, which can be misleading because it may group organisms that look alike but are not closely related evolutionarily.
In contrast, Cladistics, or cladogram analysis, is a method that focuses on the shared derived characteristics, known as synapomorphies, to establish evolutionary relationships. Cladistics assumes that characteristics change over time and uses shared derived characteristics to infer the branching sequence of a cladogram or phylogenetic tree. This method also compares ingroups and outgroups to determine the polarity of the character change, hence identifying the directionality of evolution within a clade. With the advent of molecular data, cladistics has been greatly enhanced, allowing for more precise evolutionary trees, which depict relationships based on shared ancestry rather than just superficial resemblance.