This paper is 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 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); and the third family involves particles with the same collision-coalescence kinetics but without replenishment of lost monomers. All analyses are monodisperse; only the statistics and physics of the monomers are considered. Across the range of Stokes number studied ($\mathrm{St}=0.01–3.0$), we find that the collision kernel ($K$) and the values of radial distribution function [RDF, $g\left(r\right)$] near particle contact ($r\approx d$, where $d$ is the particle diameter) of the ghost-particle (GP) system are higher than those of the coalescing systems. We show that a velocity-filtered version of the RDF $g_{\mathrm{G}}^{(-)}\left(r\right)$ is a reasonable proxy for estimating the CR system's RDF value at contact $g_{\mathrm{CR}}\left(d\right)$. We systematically report on the residual discrepancy between $g_{\mathrm{G}}^{(-)}\left(d\right)$ and $g_{\text{CR}}\left(d\right)$ as well as between the corresponding kernels $K_{\text{G}}$ and $K_{\text{CR}}$. We show that the discrepancy is due to correlation among successive collisions within the GP system by showing that a history-filtered version of the GP collision kernel, which is void of such correlations, reproduces the corresponding kernel of the coalescing systems. We introduce a collision-correlation time, ${\tau }_{\text{cc}}$, 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 $\mathrm{St}$ studied. We show that when particles with past collisions within a period comparable to ${\tau }_{\text{cc}}$ are filtered out in the GP system, the resulting history-filtered RDF ${\tilde{g}}_{\text{G}}(r;\tau \approx {\tau }_{\text{cc}})$ reproduces the RDF of the coalescing systems ($g_{\text{CR}}\left(r\right)$ and $g_{\text{CN}}\left(r\right)$). Finally, we show that among all history-bearing collisions in the GP system, the fraction of repeated collisions involving identical particles is an exponentially decaying function of $\mathrm{St}$. This work unifies the coalescing and GP systems under a single framework and affords an elegant interpretation of the former as a history filtered equivalent of the latter.

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