The dynamics of magnetic reconnection (MR) in the high-energy-density (HED) regime, where the plasma inflow is strongly driven and the thermal pressure is larger than the magnetic pressure (β>1), is reexamined theoretically and by particle-in-cell simulations. Interactions of two colliding laser-produced plasma bubbles with self-generated poloidal magnetic fields of, respectively, antiparallel and parallel field lines are considered. Through comparison, it is found that the quadrupole magnetic field, bipolar poloidal electric field, plasma heating, and even the out-of-plane electric field can appear in both cases due to the mere plasma bubble collision, which may not be individually recognized as evidences of MR in the HED regime separately. The Lorentz-invariant scalar quantity D(e) ≃ γ(e)j · (E + v(e) × B) (γ(e) = [1-(v(e)/c)(2)](-1/2)) in the electron dissipation region is proposed as the key sign of MR occurrence in this regime.