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In the first work of this series, we adopt a GW170817-like,viewing-angle-dependent kilonova model and the standard afterglow model withthe lightcurve distribution based on the properties of cosmological shortgamma-ray bursts afterglows to simulate the luminosity functions and colorevolution of both kilonovae and optical afterglow emissions from binary neutronstar (BNS) mergers. {We find that $\sim10\%$ afterglows are brighter than theassociated kilonovae at the peak time, most of which are on-axis ornearly-on-axis. These kilonovae would be significantly polluted by theassociated afterglow emission. Only at large viewing angles with$\sin\theta_{\rm v}\gtrsim 0.20$, the EM signals of most BNS mergers would bekilonova-dominated and some off-axis afterglows may emerge at $\sim5-10$\,dayafter the mergers.} At brightness dimmer than $\sim23-24$\,mag, according totheir luminosity functions, the number of afterglows is much larger than thatof kilonovae. Since the search depth of the present survey projects is$<22$\,mag, the number of afterglow events detected via serendipitousobservations would be much higher than that of kilonova events, consistent withthe current observations. {For the foreseeable survey projects (e.g., Mephisto,WFST, LSST) whose search depths can reach $\gtrsim23-24$\,mag, the detectionrate of kilonovae could have the same order of magnitude as that ofafterglows.} We also find that it may be difficult to use the fading rate in asingle band to directly identify kilonovae and afterglows among variousfast-evolving transients by serendipitous surveys. However, the color evolutionbetween optical and infrared bands can identify them, since their colorevolution patterns are unique compared with those of other fast-evolvingtransients.

Kilonova and Optical Afterglow from Binary Neutron Star Mergers. I. Luminosity Function and Color Evolution