Preaching Versus Teaching?

I have often been asked about the difference between preaching and teaching. I usually mumble that one is more informational and the other more transformational and hope that I do not get pressed too hard to explain how preaching does not involve information and how teaching is not intended for transformation. Or I might say that the difference involves delivery but again the distinction can be hard to break down. Preachers and preaching books also often want to maintain this distinction. But the older I get, I wonder about the value and validity of maintaining such a distinction. 

Hughes Oliphant Old in his magisterial work on the history of preaching states, “The earliest church understood preaching to be at the heart of its mission. The Great Commission had made it clear: “‘Make disciples of all nations, baptizing them . . . teaching [διδάσκω] them to observe all that I have commanded you’” (Matt 28:18-20)” (The Reading and Preaching of the Scriptures in the Worship of the Christian Church: Volume 1: The Biblical Period [Grand Rapids: Eerdmans, 1998], 7, my bold and insertion of Greek). This quote seems to suggest that perhaps the distinction between preaching and teaching is unimportant or at least not as great as some suggest.