If you want a more detailed definition, examining the differences in relation to the literature on Socrates, you’d be as well just to ask AI or look up some online sources. For example, Gemini says…

You're right to focus on the Socratic dialogues for this question, as that's where the terms get particularly interesting! Here's how Plato and Xenophon, who wrote most of these dialogues, used "daimon" and "daimonion" in relation to Socrates:

Daimon (δαίμων)

• Generally rare in this context: Plato and Xenophon rarely use "daimon" when specifically discussing Socrates' inner voice. They seem to reserve "daimon" for more traditional divine figures, like the gods of Olympus, or for more general discussions about spiritual beings.

Daimonion (δαιμόνιον)

• Socrates' inner voice: This is the key usage. Socrates famously describes a "daimonion" that speaks to him, a kind of inner voice or divine sign.1 It's exclusively prohibitive, meaning it only warns him against certain actions, never commanding him to do something.2

• Not a personified being: Socrates is quite vague about the nature of his daimonion.3 He doesn't describe it as a specific god or spirit with a personality.4 It's more like an intuition or a feeling, but with a divine source.

• Source of debate: Scholars still debate what exactly Socrates meant by "daimonion."5 Was it a form of conscience? Divine inspiration? Intuition honed by deep self-awareness? This ambiguity is part of what makes it so fascinating.

Why the difference?

Plato and Xenophon likely chose "daimonion" for Socrates' inner voice to distinguish it from traditional gods and daimons. By using the diminutive, they emphasized:

• Uniqueness: This was something specific to Socrates, not a standard divine being everyone had access to.

• Subtlety: The daimonion's warnings were often quiet and internal, unlike the grand pronouncements of an Olympian god.

• Moral Guidance: It was closely linked to Socrates' philosophical pursuit of virtue and the good life.6

Important Note: Even within the Socratic dialogues, there's some variation. Plato sometimes uses "daimonion" more generally, and Xenophon occasionally seems to equate it with "divine."7 But the core distinction—an inner voice specific to Socrates—remains consistent.

It's also crucial to remember that our understanding of these terms is filtered through centuries of interpretation. Christian theologians later equated "daimonion" with "demon," giving it a negative connotation that wouldn't have been prevalent in Socrates' time.

If you're interested in diving deeper into this, I highly recommend looking at the Apology, where Socrates himself discusses his daimonion, and scholarly works like those by Gregory Vlastos and Mark McPherran, who offer in-depth analyses of this enigmatic phenomenon.