The main difference between "Platonism" and "Neo-Platonism" is the concept of the One and the division of "reality" into two emanations of the One, that is, the Intellect (nous, in Greek) and the Soul (Psuche, in Greek). Platonism, which I'm going to assume we mean just Plato and not "middle-Platonism," which developed after Plato, has no concept of this division into tiers nor does it even have a concept of the One, at least according to the highly rarefied definitions that Plotinus and later Neo-Platonists would construct.

I am going to focus on the concept of the "One" here. To give a short intro to this concept, we have to remember that in Platonic thought, "what is" is "what is intelligible." Therefore, things exist not because they are embodied, corporeal, if they have an essence, or whatever; they exist because they are graspable by intellect. We also have to remember that things in our world of generation, in which things change and are in flux, must have their cause prior to their existing in our world. For example, the "horse" in this world, must have its source and its cause in the ideal form of "Horse" in that world.

If we put these together, however, we first realize that even our transcendent priors, for example, the "horse" in that realm, must have an even more transcendent prior! How did that "horse" in that realm come "into being?" Though one might simply go infinitely and never get to a source, like the endless "why's" or "how's" of a child, for Plotinus, and Neoplatonists after him, the buck stopped at "the One."

The One is both the "source" of "being," and at the same time, he is "prior" to or "above" being. One cannot say that the One "is" because it assumes that he/she/it can be analyzed in terms of existence/non-existence; he/she/it is above this duality, and indeed, all dualities, but at the same time, must be the ultimate source and cause of these dualities. Here we return to our original precept. I began by saying that for Platonists, what "is" is "what is intelligible." When Plotinus came across that which was un-intelligible, he came to the conclusion that what "is" must thus be "above being," namely, the One.

The concept of the One will undergo massive shifts, especially along the Platonists that follow Iamblichus and eventually into the developed system of Neoplatonic thought by Proclus and Pseudo-Dionysius, and indeed, by philosophers in Islamicate eras. Yet it remains possibly the most distinctive mark of Neoplatonic thought.