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 cannot be viewed solely from an ideological or affective perspective. We propose to better understand the issue polarization by approaching it as a sequential 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.