This is the first in a series of papers aimed at understanding and predicting the statistics of coalescing particles in turbulent flow, and their relation to the physics of the simpler and better-understood system of collisionless ghost-particles in turbulence. We perform three distinct families of Direct Numerical Simulations (DNS) under identical flow conditions. The first family involves ghost-particles that do not mutually interact; the second contains particles (monomers) that coalesce upon collision, with lost monomers replenished by injection of new particles at random positions to maintain a constant monomer density (CR); the third family involves particles with the same collision-coalescence kinetics but without replenishment of lost monomers (CN). All analyses are monodisperse–only the statistics and physics of the monomers are considered. Across the range of Stokes number studied (St = 0.01–3.0), we find that the collision kernel (K) and the values of radial distribution function (RDF, g(r)) near particle contact (r ≈ d, where d is the particle diameter) of the ghost-particle system are higher than those of the coalescing systems. We show that a velocity-filtered version of the RDF gG(−)(r) is a reasonable proxy for estimating the CR system’s RDF value at contact gCR(d). We systematically report on the residual discrepancy between gG(−)(d) and gCR(d) as well as between the corresponding kernels KG and KCR. We show that the discrepancy is due to correlation among successive collisions within the ghost-particles system – by showing that a history-filtered version of the ghost-particle collision kernel, which is void of such correlations, reproduces the corresponding kernel of the coalescing systems. We introduce a collision-correlation time, τcc, to quantify how long current collisions influence future collision events and show that it is finite and has a narrow range across the range of St studied. We show that when particles with past collisions within a period comparable to τcc are filtered out in the ghost-particle system, the resulting history-filtered RDF g̃G(r; τ ≈ τcc) reproduces the RDF of the coalescing systems (gCR(r) and gCN(r)). Finally, we show that among all history bearing collisions in the ghost-particle system, the fraction of repeated collision involving identical particles is an exponentially decaying function of St. This work unifies the coalescing and ghost particle systems under a single framework and afford an elegant interpretation of the former as a history filtered equivalent of the latter.