I am not so sure the early church had a clear line of demarcation between the two. Teaching can clearly become preaching and vice versa.
Notice the interchangeableness of the terms in these parallel gospels.
Mat 28:19 Go ye therefore, and
teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Mar 16:15 And he said unto them, Go ye into all the world, and
preach the gospel to every creature.
Mar 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Col 1:28 Whom we preach, warning every man, and teaching every man in all wisdom; that we may present every man perfect in Christ Jesus:
Act 5:42 And daily in the temple, and in every house, they ceased not to teach and preach Jesus Christ.
Would you say that the ministry referred to in
Eph 4:11 was not preachers?