  Context. 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 < TJ < 3)
orbits. Aims. This investigation aims to examine the orbital dynamics of JFCs
and comet-like fireballs over 10,000 yr timescales, focusing on the
trajectories and stability of these objects in the context of gravitational
interactions within the solar system. Methods. We employed an extensive
fireball dataset from the 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. Results. The analysis
confirms frequent Jupiter encounters among most JFCs, inducing chaotic orbital
behavior with limited predictability and short Lyapunov lifetimes (about 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% on ``JFC-like'' orbits shown not to be
prone to frequent Jupiter encounters; in particular, only 1-5% of all fireballs
detected by the four networks exhibit dynamics similar to that of actual JFCs.
In addition, 22% (16 of 72) of near-Earth JFCs are on highly stable orbits,
suggesting a potential main belt origin for some of the bodies.
