We present a comparison of the spatial distributions of Ly$alpha$ emitters (LAEs) and massive star-forming and quiescent galaxies (SFGs and QGs) at $2<z<4.5$. We use the photometric redshift catalog to select SFGs and QGs and a LAE catalog from intermediate/narrow bands obtained from the Subaru Telescope and Isaac-Newton Telescope in Cosmic Evolution Survey (COSMOS). We derive the auto-/cross- correlation signals of SFGs, QGs, and LAEs, and the galaxy overdensity distributions at the position of them. Whereas the cross-correlation signals of SFGs and QGs are explained solely by their halo mass differences, those of SFGs and LAEs are significantly lower than those expected from their auto-correlation signals, suggesting that some additional physical processes are segregating these two populations. Such segregation of SFGs and LAEs becomes stronger for rest-frame ultraviolet faint LAEs ($M_{rm UV}>-20$). From the overdensity distributions, LAEs are located in less dense regions than SFGs and QGs, whereas SFGs and QGs tend to be in the same overdensity distributions. The different spatial distributions of LAEs compared to those of massive galaxies may be attributed to assembly bias or large amounts of neutral hydrogen gas associated with massive halos. These results reinforce the importance of exploring multiple galaxy populations in quantifying the intrinsic galaxy environment of the high-$z$ universe.
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