Various assessments have contributed to inconsistent findings regarding the correlation between core stability and vertical jumps. Therefore, this study aimed to re-examine this correlation based on novel core stability assessments. Twenty-one recreationally active male college students (age, 21.7 ± 2.1 years; stature, 174.9 ± 6.7 cm; body mass, 67.7 ± 7.8 kg; leg length, 88.9 ± 4.8 cm; arm length, 87.8 ± 4.0 cm) participated in this experiment. Core stability was divided into static and dynamic core stabilities, with the static core stability measured using the Eight-Level Prone Bridge and Five-Level Side Bridge tests and the dynamic core stability measured using the Y Balance Test (YBT). These tests comprehensively evaluate core stability as it is defined. Kinematic and kinetic data on vertical jumps were collected to provide process information beyond the outcome performance. Subsequently, these data were correlated with core stability for a deeper insight into the relationship between core stability and the process and outcome performance of vertical jumps. The main results revealed that the Eight-Level Prone Bridge demonstrated moderate to substantial correlations with Δ F_y, Δ I_y, ΔD_{left knee z}, and ΔD_{left ankle y} (−0.62 ≤ r ≤ 0.52); the Five-Level Side Bridge exhibited moderate correlations with Δ F‾, Δ F‾, Δ I, Δ I, ΔD, and ΔD (−0.52 ≤ r ≤ 0.59); YBT displayed moderate correlations with F_z, F_{left z}, ΔD_{left ankle y}, ΔD_{right ankle y}, ΔD_{left ankle z}, Δ D_{right ankle z}, NΔT_{ankle y}, and N T_{left ankle z} (−0.54 ≤ r ≤ 0.54) during the propulsive phase of vertical jumps. However, no significant correlations were observed between static/dynamic core stability and jumping height. Therefore, individuals with greater core stability should experience improved process performance (better movement quality), although this benefit is ineffective in translating into jumping height improvement due to impaired explosive features. Coaches may consider core stability in training to trigger an improved process performance of the vertical jump when the technique is the key issue to be solved, although future studies are required to verify this further.