What's the difference between a "primordial consciousness" and a soul?

It seems certain Buddhist groups have come to believe in something they call the "luminous mind " or the "primordial consciousness"; in essence, a mind that is lasting, stable, and assumedly pleasant. From a Theravada point of view, this is terribly problematic; if this mind is able to know multiple consecutive objects, then it is indistinguishable from multiple cittas arising and ceasing, and thus not lasting at all. The idea that there is something lasting from moment to moment sounds very much like the concept of a soul. How does it differ? Or is the point that these Buddhists do believe in a soul?