Platonists, Paleo and Neo. I have a question for you.

I am working on a novel that takes place in Renaissance Rome and â€" besides a lot of sex and violence -- has various characters discussing Neo-platonism (although they don't call it that). There seem to be a couple of specialists here who are more familiar with neo-platonism then I am and so I'd be grateful for some guidance.
As I understand it, Neoplationism, in its various permutations, refers to the presence of the 'divine' (whatever that is) in humans and nature. That being the case, how do we separate out Neo-platonism from pantheism, Christian mysticism, sufism, New-age-ism, animism, and just plain voodoo?

What, specifically, is 'platonic' about Neo-platonism, that distinguishes it from all the other forms of divine immanence?

Cartomancer? Brian? MPhil? Anyone?

Help would be much appreciated.