We carry out systematic and dedicated experimental investigations on the shot-to-shot coherence and wave-packet formation in quasi-mode-locked (QML) regimes, including noise-like-pulse, symbiotic, and multi-soliton regimes in an anomalous-dispersion fiber ring cavity. To analyze the regimes in real-time, we take advantage of the spatio-temporal shot-to-shot measurement technique. We show that the individual regimes exhibit significantly different coherence characteristics, depending not only on the amount of nonlinear phase shift accumulated per roundtrip but also on the degree of soliton interaction, the latter of which crucially governs the bunching (i.e., the wave-packet formation) or anti-bunching mechanisms in the corresponding QML regimes. In fact, solitons with higher intensities tend to undergo higher nonlinear phase shift and stronger soliton interactions. Subsequently, the intensified soliton interactions among the individual solitons in the multi-soliton-regime cavity trigger them to form a bunched soliton-group, i.e., a wave packet, thereby resulting in QML pulses in the noise-like pulse or symbiotic regime. This complicated nonlinear process, in turn, causes a severe degradation in the shot-to-shot coherence of the resultant QML pulses. In addition, the shot-to-shot coherence trends observed in the experiment are in good agreement with our previous numerical predictions, so that the strong correlation between the shot-to-shot coherence of QML pulses and the corresponding nonlinear phase shift accumulated per roundtrip is confirmed by this experimental observation.