Jupiter-family comets (JFCs), which originate from the Kuiper belt and scattered disk, exhibit low-inclination and chaotic trajectories due to close encounters with Jupiter. Despite their typically short incursions into the inner solar system, a notable number of them are on Earth-crossing orbits, with fireball networks detecting many objects on ``JFC-like'' ($2<T_ J <3$) orbits. This investigation aims to examine the orbital dynamics of JFCs and comet-like fireballs over $10^ $\,yr timescales, focusing on the trajectories and stability of these objects in the context of gravitational interactions within the solar system. We employed an extensive fireball dataset from Desert Fireball Network (DFN), European Fireball Network (EFN), Fireball Recovery and InterPlanetary Observation Network (FRIPON), and Meteorite Observation and Recovery Project (MORP), alongside telescopically observed cometary ephemeris from the NASA HORIZONS database. The study integrates 646 fireball orbits with 661 JFC orbits for a comparative analysis of their orbital stability and evolution. The analysis confirms frequent Jupiter encounters among most JFCs, inducing chaotic orbital behavior with limited predictability and short Lyapunov lifetimes (sim 120 years), underscoring Jupiter's significant dynamical influence. In contrast, "JFC-like" meteoroids detected by fireball networks largely exhibit dynamics divergent from genuine JFCs, with 79-92<!PCT!> on ``JFC-like'' orbits shown not to be prone to frequent Jupiter encounters; in particular, only 1-5<!PCT!> of all fireballs detected by the four networks exhibit dynamics similar to that of actual JFCs. In addition, 22<!PCT!> (16 of 72) of near-Earth JFCs are on highly stable orbits, suggesting a potential main belt origin for some of the bodies. This extensive study delineates the stark dynamical contrast between JFCs and JFC-like meteoroids detected by global fireball networks. The majority of centimeter- and meter-scale meteoroids on JFC-like orbits exhibit remarkably stable trajectories, which starkly differ from the chaotic paths of their km-scale counterparts. Our findings suggest that the JFC-like objects observed by fireball networks predominantly originate from the outer main belt, with only a minor fraction being directly attributable to traditional JFCs.