  In this paper we present an example of two polarized K3 surfaces which are
not Fundamental Group Equivalent (their fundamental groups of the complement of
the branch curves are not isomorphic; denoted by FGE) but the fundamental
groups of their related Galois covers are isomorphic. For each surface, we
consider a generic projection to CP^2 and a degenerations of the surface into a
union of planes - the "pillow" degeneration for the non-prime surface and the
"magician" degeneration for the prime surface. We compute the Braid Monodromy
Factorization (BMF) of the branch curve of each projected surface, using the
related degenerations. By these factorizations, we compute the above
fundamental groups. It is known that the two surfaces are not in the same
component of the Hilbert scheme of linearly embedded K3 surfaces. Here we prove
that furthermore they are not FGE equivalent, and thus they are not of the same
Braid Monodromy Type (BMT) (which implies that they are not a projective
deformation of each other
