(Biological) Taxonomy is a concept about easy to classify organism species and groups based on morphology (example: embryo, phenotypes), genes (exmple: 18S ribosome rna), palynology, anatomy, biochemistry and evolutionary relationship. Each (biological) groups has classification hierarchy. Nowdays, many biologists use clades instead of taxonomic ranks.
Each taxonomy/nomenclatural ranks & scientific names use ancient language, Latin. This language is also used on Medicine and others such as religion or media.
Phylogeny is a tree diagram that shows about shared morphological traits, evolutionary and genetic relationships of each groups and species, which it can helps to solve the puzzle. Also in fact, phylogeny is actually based from an ancient idea "Tree of Life".
There's types and difference of each phylogeny tree diagrams, rooted & unrooted, labeled and unlabeled, and mathematical enumerating tree diagram. Rooted ones does includes common ancestor (root), which can helps for evolutionary relationship, Unrooted ones does not show common ancestor, which is slightly hard & unhelpful to some peoples.
Also there's 8 types of special phylogeny tree diagrams, Dendrogram, Phylogram, Cladogram, Chronogram, Dahlgrenogram, Phylogeny network, Spindle Phylogeny and Coral diagram.
Rooted tree.
Unrooted tree.
SOON!