Final answer:
The correct term for the orderly arrangement of organisms that reflects their evolutionary history is Phylogenetic Classification, represented by phylogenetic trees.
Step-by-step explanation:
The orderly arrangement of organisms into groups that indicate evolutionary relationships and history is known as Phylogenetic Classification. Scientists use a tool called a phylogenetic tree to show the evolutionary pathways and relationships between organisms. A phylogenetic tree is a diagram used to reflect evolutionary relationships among organisms or groups of organisms, considering various traits and genetic information. It forms the basis of the modern systematics field, which organizes and classifies organisms based on these evolutionary relationships. Unlike the earlier taxonomic classification system that primarily grouped organisms based on physical similarities, phylogenetic classification incorporates evolutionary history to provide a more accurate representation of the organisms' lineage and ancestry.