Is there a difference in the Pali language between "intention" (as in Right Intention) and "motivation"?
I think that "right intention" (or "resolve") is connected with a sense of purpose -- with "purpose" meaning, for example, "I do this, in order to (for the purpose of, with the intention to) accomplish that".
I think that "right intention" is the second factor of the path and that it's closely related with "right view". I think that "right view" would explain why you want to do something, and could therefore be described as the "motive" for subsequent intention.
Similarly "wrong view" conditions wrong intention and so on.
harmlessness seems to be more passive and therefore maybe not a motivation in the same way
One of the doctrines of harmlessness is Chapter 10 of the Dhammapada, the first verse:
All tremble at violence; all fear death. Putting oneself in the place of another, one should not kill nor cause another to kill.
To relate that to intention, I'd say that "Putting oneself in the place of another" is a view, and that the consequence of that view is the "intention" to be harmless (and, consequently, harmless actions).
Also I think that "harmlessness" and "good-will" are closely related, two sides of the same coin. I can barely tell them apart. Also you say it's "not a motivation" but I think that's a motive of all ethics (sila):
[By abandoning the taking of life, abandoning stealing, abandoning lying, illicit sex, and the use of intoxicants] ... the disciple of the noble ones ... gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings. In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression ... [these are the five gifts] — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that is not open to suspicion, will never be open to suspicion, and is unfaulted by knowledgeable contemplatives & brahmans. And [these are the rewards of merit], reward of skillfulness, nourishment of happiness, celestial, resulting in happiness, leading to heaven, leading to what is desirable, pleasurable, & appealing; to welfare & to happiness.
You might be asking for the "sense of samvega" though (which is mentioned in Saptha Visuddhi's answer, see also for example here). I think that samvega is understood to mean not only a sense of dismay, perhaps as a result of view again, but also a sense of (purposeful) urgency.
And I think that samvega is associated with virya (translated as energy and, as you mentioned, effort).