The qualitative difference between the anomalous scaling properties of hadronic final states in soft and hard processes of high energy collisions is studied in some detail. It is pointed out that the experimental data of e + e − collisions at E cm =91.2 GeV from DELPHI indicate that the dynamical fluctuations in e + e − collisions are isotropical, in contrast to the anisotropical fluctuations oberserved in hadronhadron collision experiments. This assertion is confirmed by the Monte Carlo simulation using the Jetset7.4 event generator.PACS number: 13.85 Hd Keywords: Multiparticle production, Hard and soft processes, Dynamic fluctuations, Self-affine fractal Quantum Chromodynamics (QCD) [1] as a candidate of the basic theory of strong interaction has been very successful in the study of hard processes, such as scaling violation in deep inelastic scattering (DIS), hadronic-jet production in e + e − annihilation, large-p t -jet production in hadron-hadron collisions etc.. In such processes there exist large scales so that QCD can be solved perturbatively due to asymptotic freedom.On the contrary, in soft-hadronic processes, e.g. hadron-hadron, hadron-nucleus and nucleus-nucleus collisions below CERN collider energies, there is no large scale present, and the interaction becomes so strong that pQCD is no longer applicable. In these cases, the problem is hard to be solved analytically from the first principle and phenomenological regularities extracted from experiments have to be ultilized to increase our knowledge on the property of the basic dynamics in such processes.In this respect, a comparison of the phenomenology of multiparticle final states in soft and hard processes is worthwhile. Such comparison is helpful in getting information about the similarity and distinction between the dynamics of particle production in these two kinds of processes. In particular, to find out the qualitative differences, if any, between them is especially interesting.In this paper we will show that such a qualitative difference does exist in the anomalous scaling property of final-state particle distribution. It turns out that the higher-dimensional factorial moments (FM) do have anomalous scaling property (obey a power law with the diminishing of phase space) when and only when the partition of phase space is anisotropic for soft processes while isotropic for hard ones. This means that the dynamical fluctuations are anisotropic in the former case while isotropic in the latter. This qualitative distinction may serve as a useful criterion in the study of the basic dynamics of particle production in these two kinds of processes.Let us first review briefly the status of dynamical-fluctuation study in high energy collisions [2]. The interest in this study was first stimulated by the experimental finding in 1983 of unexpectedly large local fluctuations (2 times the average) in a high multiplicity event from JACEE [3]. The same phenomena were observed latter also in accelerator experiments, the local fluctuations being as large as...