Anunciata:
The Didache was an instruction Manuel - Covered everything from basic doctrine to practical and ethical questions.
But the writings of the Church Fathers are usually refered to as “Patristic” Writings - “Patristics” are usually divided into Sub-Apostolic Fathers, Ante-Nicene Fathers and Post-Nicene Fathers.
The Sub-Apostolic Fathers (e.g., St. Polycarp of Smyna, Pope St. Clement of Rome, The Didache) are usually dealing with very basic issues and with persecution.
The Ante-Nicene Fathers (e.g., St. Irenaeus, Origen, St. Hippolytus) are usually dealing with more complicated issues and persecution.
The Post-Nicene Fathers (e.g., St. Athanasius of Alexandria, Pope St. Gregory the Great, St Augustine) are usually dealing with heresies, Ecumenical Councils and the Collapse of Secular Society.
The Didache forms a very small part of this huge volume of literature.
I hope this helps ease some of the confusion.
In Christ, Michael