When discussing the difference between an agent by nature and an agent by will, it seems like God and knowledge should play key roles.
God and nature seem to go hand and hand for Averroes. He appears to view God as the ultimate cause. He seems to see nature as proof of God’s all-powerful wisdom.
A natural agent seems to be aligned with the naturalness of God. God is essential, and an agent by nature performs something essential. As Averroes says about natural agents, they perform “one thing and this essentially.” He goes on to provide examples, like that coldness makes cold and heat leads to warmth. There is a clear, taut link when it comes to agents by nature. There’s a fundamental rhyme and reason.
As for an agent by will, you might claim that this type of agent is separate from God. According to Averroes, the agent who “chooses and wills lacks the things which he wills.” Of course, God cannot “lack anything He wills.” In other words, if God was missing something, God wouldn’t be God. The agent by will is, in a way, marking its separation from nature because it’s making a choice between the “better of two things.” Again, God does not need a “better” condition. From Averroes’s view, it doesn’t get better than God.
In brief, you could argue that the agent of will acts from knowledge. while the agent of nature acts irrespective of knowledge. The latter reflects an Edenic state where knowledge isn’t required. The former point to humanity’s postlapsarian position, where knowledge is conspicuously present.