  By extending our {\it victory} implementation of the parquet approach to
include non-local Coulomb interactions, we study the extended Hubbard model on
the two-dimensional square lattice with a particular focus on the competition
of the non-local charge and spin fluctuations. Surprisingly, we find that their
competition, as the mechanism driving the phase transition towards the charge
density wave, dominates only in a very narrow parameter regime in the immediate
vicinity of the phase transition. Due to the special geometry and the Fermi
surface topology of the square lattice, antiferromagnetic fluctuations dominate
even for sizable next-nearest neighbor interactions. Our conclusions are based
on the consistent observations in both the single- and two- particle
quantities, including the self-energy, the single-particle spectral function,
the two-particle susceptibility, the density-density vertex function and the
optical conductivity. Our work unbiasedly establishes the connection of these
quantities to the charge fluctuations, and the way of interpretation can be
readily applied to any many-body method with access to the two-particle vertex.
