Well-formedness vs weak well-formedness

The literature contains two definitions of well formed varieties in weighted projective spaces. By the first, a variety is well formed if its intersection with the singular locus of the ambient weighted projective space has codimension at least 2. By the second, a variety is well formed if it does not include a singular stratum of the ambient weighted projective space in codimension 1. We show that these two definitions differ indeed, and show that they coincide for the quasismooth weighted complete intersections of dimension at least 3.