Speaking my own mind without consulting the suttas, here is my offering...
Ill will is more subtle than the intention of harmfulness and precedes it. One could have ill will towards form, for example when one feels a tearing sensation in one's knee whilst walking or meditating and ill will arises. The remedy for ill-will is loving-kindness.
The intention of harmfulness is more gross than ill will and is subsequent to it. One could have harmfulness towards form as in the above example; the difference is that there is anger arising relatively concurrently to it. The remedy for ill-will is compassion.
The reason I give for this is that loving-kindess is the first brahmavihara and compassion is the second. Loving-kindness is necessary for compassion and thus ill will is necessary for harmfulness.
I hope that helps and I hope someone comes along to clarify this with words of Dhamma
Then the Lord said to the monks: 'Now, monks, I declare to you: all conditioned things are of a nature to decay - strive on untiringly.' These were the Tathagata's last words.
-DN 16, trans. Maurice Walshe
'Whatever should be done, bhikkhus, by a compassionate teacher out of compassion for his disciples, desiring their welfare, that I have done for you. These are the feet of trees, bhikkhus, these are empty huts. Meditate, bhikkhus, do not be negligent, lest you regret it later. This is our instruction to you.'
-SN 43.1, trans. Ven. Bhikkhu Bodhi