Event‐to‐event intraseasonal convection is found to be significantly different from a canonical Madden‐Julian oscillation (MJO). Nearly half of all austral summer events do not show the same initiation or propagation characteristics of canonical MJOs, although they meet some MJO criteria during their life cycles. Variations of intraseasonal convection fall within three distinct forms: the canonical MJO, an eastward decaying mode, and an eastward intensifying mode. This distinction offers important insights into the overall dynamics and predictability of tropical intraseasonal variability. Sea surface temperature anomalies generated during convective breaks are fundamental for canonical propagation and result from radiative forcing whose modulation is a consequence of large‐scale wave dynamics. Eastward propagation seems to rely more on the state of the tropical atmosphere‐ocean system before convective triggering than on the trigger itself. Eastward decaying events exhibit weaker wave‐related anomalies. Alternatively, mechanisms driving intensification over Indonesia are very different from the first two categories.