Q. What is the difference between neo-advaita (or ‘radical non-duality’) and traditional advaita. Or are they just pointing to the same thing in different ways?
Tom: There is an essential difference.
This essential difference is one of SADHANA, or spiritual practice, and SUFFERING.
Neo-Advaita states there is no separate person or jiva that could engage in any sadhana, and that any sadhana perpetuates the illusion of duality. Neo-Advaita also does not claim to end suffering.
(Traditional) Advaita emphasises the importance of sadhana as being absolutely necessary (for most) in order to realise the Self and go beyond and END all suffering and duality.