Polarization is often a cliché, its conceptualization remains approximate and no consensus has been reached so far. Often simply seen as an inevitable result of the use of social networks, polarization nevertheless remains a complex social phenomenon that must be placed in a wider context. To contribute to a better understanding of polarization, we approach it as an evolving process, drawing on a dual expertise in political and data sciences. We compare the polarization process between one mature debate (COVID-19 vaccine) and one emerging debate (Ukraine conflict) at the time of data collection. Both debates are studied on Twitter users, a highly politicized population, and on the French population to provide key elements beyond the traditional US context. This unprecedented analysis confirms that polarization varies over time, through a succession of specific periods, whose existence and duration depend on the maturity of the debate. Importantly, we highlight that polarization is paced by context-related events. Bearing this in mind, we pave the way for a new generation of personalized depolarization strategies, adapted to the context and maturity of debates.