Kerusso means "to proclaim". One can proclaim anything to anybody in any situation. Therefore, a Christian can proclaim things (truths, doctrines, promises, fulfillments, or even next week's dinner on the grounds) to the assembly.
Euaggelizo means to bring good news. It is used in Greek for practically any kind of announcing or bringing good news. In fact there are instances in Greek literature of the word being used to refer to announcing or bringing BAD news. So it basically means simply to bring news to another. Therefore Christians can euaggelizo to the congregation.
Marturion means to speak as a witness, to testify (as a witness in a legal proceeding), to state X happened and you affirm that X is true. Therefore Christians can testify to the assembly of believers.
"Preach" (the English word) means the following:
PREACH, verb intransitive [Latin proeco, a crier; precor.]
1. To pronounce a public discourse on a religious subject, or from a subject, or from a text of Scripture. The word is usually applied to such discourses as are formed from a text of Scripture. This is the modern sense of preach
2. To discourse on the gospel way of salvation and exhort to repentance; to discourse on evangelical truths and exhort to a belief of them and acceptance of the terms of salvation. This was the extemporaneous manner of preaching pursued by Christ and his apostles.
Matthew 4:10.
Acts 10:14.
PREACH, verb transitive To proclaim; to publish in religious discourses.
What ye hear in the ear, that preach ye on the house-tops.
Matthew 10:7.
The Lord hath anointed me to preach good tidings to the meek.
Isaiah 61:1.
1. To inculcate in public discourses.
I have preached righteousness in the great congregations.
Psalms 40:9.
He oft to them preach'd
Conversion and repentance.
To preach Christ or Christ crucified, to announce Christ as the only Savior, and his atonement as the only ground of acceptance with God.
1 Corinthians 1:17.
To preach up, to discourse in favor of.
Can they preach up equality of birth?
PREACH, noun A religious discourse. [Not used.]
(Webster's 1828)
Thus the use of "preach" in
Acts 20:7 and
Acts 20:9 for the Greek term meaning to discouse, dialogue, or dispute.
There is no linguistic OR theological categories of "preaching vs teaching". One can proclaim, bring good news, and testify while teaching. One can teach while proclaiming, announcing good news, and/or giving testimony. One can do these things to unbelievers, believers, or even to oneself, in church, out of church, verbally, written, sign language, in person, by video or audio, in person, by proxy, live, or pre recorded, with or without flannelgraphs even.
The subject here is literally moot. One can preach loudly or quietly, one can teach loudly or quietly, one can preach while teaching, and vice versa.