The bosonic Josephson junction, one of the maximally simple models for periodic-driven many-body systems, has been intensively studied in the past two decades. Here, we revisit this problem with five different methods, all of which have solid theoretical reasoning. We find that to the order of ω^{-2} (ω is the modulating frequency), these approaches will yield slightly different effective Hamiltonians. In particular, the parameters in the effective Hamiltonians may be unchanged, increased, or decreased, depending on the approximations used. Especially, some of the methods generate new interactions, which still preserve the total number of particles, and the others do not. The validity of these five effective models is verified using dynamics of population imbalance and self-trapping phase transition, and we find that the method based on the rotating frame by a unitary transformation has the highest accuracy. The difference between these methods will become significant when the driving amplitude or interaction strengths are comparable with the driving frequency. These differences can also be manifested from their long-time dynamics. We demonstrate this physics using a Bose-Josephson junction, and it is to be hoped that the validity of these methods and their tiny differences put forward in this paper can be verified in realistic experiments in the future using quantum simulating platforms, including but not limited to ultracold atoms.