A recent study categorized the Madden-Julian Oscillation (MJO) during the boreal winter season into four types including stand, jump, slow eastward propagating, and fast eastward propagating MJO. This study focuses on the stand and jump MJO events. Based on whether their convection penetrates the Maritime Continent (MC), stand and jump MJO are combined as non-penetrating (NP) MJO, while the rest two types are combined as eastward-penetrating (EP) MJO. Results reveal the relative roles of the westward-propagating wave (WPW), as well as the QBO and ENSO, in limiting MJO propagation. Lack of the pre-moistening over the southern sea surface of MC is responsible for NP MJO’s failure to penetrate MC. The active convection of WPW hinders the NP MJO descending branch over the Pacific and therfore leads to the insufficient meridional advective moistening over the southern sea surface of the MC. The overall drying over the MC for jump MJO also comes from the intraseasonal dry amonalies induced by WPW over the western Pacific, which are then advected to MC by the superposed seasonal mean northern easterlies. The independent convection over the Pacific for jump MJO is influenced by a combined effect of the QBO and ENSO. Under the influence of the preferred QBO westerly (QBOW) phase, the tropopause instability of NP MJO is decoupled with its convection. The decoupled tropopause instability propagates eastward into the Pacific, and amplifies the local WPW convection there for jump MJO. For stand MJO, however, the La Nina-like seasonal mean cool sea surface temperature (SST) anmalies confine WPW within the western Pacific. Therefore, the decoupled tropopause instability of stand MJO is out phase of WPW over the central Pacific, and fails to induce an independent convection as a result. The similar diagnosis is further applied to the CESM2 and E3SM CMIP6 historical simulations to investigate the MJO diversity and propagation in climate models. Four MJO types as in the observation are successfully categorized in these two models. The accompanied westward propagating waves over the central-western Pacific for NP MJO events are also evident. However, models suffer from some biases in MJO propagation such as too many NP MJO events than the observation.