Didaché = the established content or doctrine that has been taught. It's the "what" — the teaching as a finished product
Summary from both sources:
Didaché = the established content or doctrine that has been taught. It's the "what" — the teaching as a finished product or body of truth . Didaché can refer to a sermon, a specific lesson, or the entire body of Christian truth. Context determines the emphasis. In Mark
1:27, the people marvel at a specific instance of teaching that included a command over unclean spirits.
And they were all amazed, insomuch that they questioned among themselves, saying, What thing is this? what new doctrine is this? for with authority commandeth he even the unclean spirits, and they do obey him.
Mark 1:27, KJV Here, didaché kainē — "new teaching" or "new doctrine" — refers to the novel and powerful nature of Jesus' specific instruction combined with demonstrative authority. It is an event. Yet in Romans 6:17, Paul uses didaché to refer to a fixed form of teaching that shapes obedience.
But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.
Romans 6:17, KJV The phrase "form of doctrine" — typon didachēs — indicates a pattern, a mold, or a standard. The Roman believers had not obeyed a vague religious impulse. They had obeyed a specific, defined didaché that was "delivered" or "handed down" to them. This implies an objective body of truth that existed prior to their faith and to which their faith conformed. Didaché , then, is not invented by the community; the community is formed by the didaché .
The writer of Hebrews uses didaché in the plural to refer to foundational categories of Christian instruction that every believer should master before moving on to maturity.