We present a study of p (p) over bar collisions at roots=1800 and 630 GeV collected using a minimum bias trigger by the CDF experiment in which the data set is divided into two classes corresponding to "soft" and "hard" interactions. For each subsample, the analysis includes measurements of the multiplicity, transverse momentum (p(T)) spectrum, and the average p(T) and event-by-event p(T) dispersion as a function of multiplicity. A comparison of results shows distinct differences in the behavior of the two samples as a function of the center of mass (c.m.) energy. We find evidence that the properties of the soft sample are invariant as a function of c.m. energy.