As far as I know, the explicit term “nondualism” was first used in certain strands of Mahayana Buddhism. I believe it later was adopted by the Vedanta school of Hindu scholastic philosophy. I was fascinated with these as a young man, and was for a time much absorbed in developing a sort of Alan Watts style interpretation of Plotinus’ emphasis on the One as a similar kind of radical nondualism.
Radical nondualism goes beyond the rejection of sharply dualist views like those of Descartes on mind and world, and the different religious dualisms like those of Augustine, the Zoroastrians, the Gnostics, the Manichaeans, or the Samkhya school of Hinduism. Each of these latter has important differences from the others, but what unites them is the strong assertion of some fundamental duality at the heart of things. Radical nondualism aims to consistently reject not only these but any vestige of duality in the basic account of things.
The point of view I would take now is that many useful or arguably necessary distinctions are often formulated in naive, overly blunt ways. We should strive to overcome our naivete and our excessive bluntness, but that does not in any way mean we should try to overcome distinction per se. There can be no meaning — even of the most spiritual sort — without some sort of distinction between things. “All is One” is at best only a half-truth, even if it is a profoundly spiritual one.