What you are otherwise referring to are, for example, prestressed concrete precast slabs. However, their construction is completely different and they cannot be concreted in place (but they also have a chamfer, at least the ones I have seen so far )
Yes, prestressed concrete precast slabs are "complete" in that sense, as no cast-in-place concrete is "missing" on them. A chamfer is safer: it does not weaken the component where that would be problematic and is not as delicate as a right-angled corner, which would be more prone to chipping.
The element slab always needs to be supplemented with cast-in-place concrete.
Other semi-precast slab variants, as I mentioned and which were also called element slabs, have become less significant in the market since the "filigree slab" has established itself. It is actually logical that the term thus "freed up" for new interpretations is now gladly used for "filigree slabs from other manufacturers." Element slab is a generic term and as such not protectable, whereas Filigrandecke (R) to my knowledge is a trademark of one manufacturer, against whose warnings competitors probably have no appetite. Haha, I just noticed that the search function in the trademark register of the DPMA is similarly "in need of improvement" as that of this forum
By the way, element slabs as semi-precast slabs are also available from several brick manufacturers, all of which must be completed with cast-in-place concrete.