口調 and 口頭: tone of voice and oral delivery
Compare a gentle explanation to a child with an explanation delivered orally. A change in a phone conversation’s tone differs from a change between speech and writing.
The tone of speaking
口調 (くちょう) means tone or manner of speaking. 「彼は穏やかな口調で子供に事情を説明した。」 says he explained the situation to a child in a gentle tone.
「電話の相手の口調が急に厳しくなった。」 says the person on the other end of the phone suddenly sounded stern. The change concerns tone; the sentence does not further identify the person or the call’s direction.
Delivery through speech
口頭 (こうとう) means oral delivery. 「担当者から口頭で簡単な説明を受けた。」 says a brief spoken explanation was received from the staff member.
「変更点は口頭ではなく書面で伝えてください。」 requests conveying changes in writing rather than orally. It concerns delivery method rather than tone.
Two properties of the same utterance
An oral explanation can have a gentle or stern tone. Whether it is 口頭 and what its 口調 is are different properties that can apply together.
A gentle explanation does not mean a switch to written delivery, and a request for writing does not mean a request to sound gentler. Identify the property the sentence addresses.
Does 「電話の相手の口調が急に厳しくなった。」 describe a change in delivery method or in tone?
Show the answer and why
In tone. The person’s way of speaking suddenly became stern; a switch to written delivery is not stated.