Fast response from Chris. We had basically come to the right answer.
International: overtaking is included in 34(a), and 34(c) is for when you need to other vessel to move aside.
Inland: Overtaking is not included in 34(a), but the Inland sound signals are the same in 34 (a) and (c)
Chris's Complete Response"
34(a) applies to power-driven vessels making maneuvers authorized or required by the Rules, to wit, turning right or left or operating astern propulsion
. You are right that this includes maneuvers made while overtaking, but the whistle signal required by (a) does not tell the other vessel anything about passing on one side or the other, only that it is turning.
The Rule 34(c) signal does not tell the other vessel that you are going to take the overtaking action, only that you are proposing to take that action. The overtaken vessel then is required to either give its assent before you begin to overtake, or to disagree with your proposal, by returning the 34(d) doubt signal - five or more short blasts). Remember that International Rule 34(c) only applies when overtaking in a narrow channel, and does not apply in open waters with no draft
constraints. Rule 9(e), concerning passing in narrow channels or fairways, is the Rule that requires the giving of the Rule 34(c) signals, and it is Rule 9(e) that requires the signal only if the vessel to be overtaken "has to take action to permit
The Inland Rule 34 is not at all like the International Rule 34; you should not try to understand them together. They are completely different rules, even though they have the same numbers and concern sound signals. Figure 3 is not an overtaking situation; it is a crossing at a narrow angle, and the two pictures are of the same crossing vessels, but at different times. Figure 3 illustrates what the term "leave" means, as in leaving the other vessel to either port or starboard. When crossing at narrow angles, "leaving" may seem ambiguous. Inland Rule 34(a) applies only to meeting and crossing; Inland 34(c) applies to overtaking.
The Inland Rule signals used for meeting and crossing are the same as the Inland signals for overtaking, and therefore potentially ambiguous, but that's what the Inland mariners (advisory panel) wanted when the current
Inland Rules were drafted, because that's what they had been doing.
Also, keep in mind that the maritime term "passing" does not mean the same thing as "passing" applied to motor
vehicles on roads. The maritime rule term "passing" simply means going past another vessel, whether that happens when meeting, crossing, or overtaking. That may be one of the causes for your confusion. "Passing" and "overtaking" are not interchangeable.
I hope this helps. Good luck!