Political polarization, seen as a key threat to contemporary democracy, has been tied to the rise of digital social media. However, how this process develops in the context of a social media environment characterized by multiple platforms—with differing norms, contents, and affordances—has not been sufficiently explored. In the present article, we propose a distinction between positional polarization, that is, people’s view on a political issue, and interpretative polarization, that is, how that political issue is contextualized and understood. We use this distinction to examine an issue of political controversy in Israel, examining how polarization develops over time, on three social media platforms—Facebook, Twitter, and WhatsApp. We find that contrasting positions are strongly connected to conflicting interpretations, both of which are clear from the start, with only minor overtime shifts. Moreover, while sharing broad similarities, the three platforms show a few distinctive polarization dynamics—both positional and interpretative—that can be connected to their varied socio-technical affordances. The study advances our theoretical understanding of polarization by examining how different social media platforms may shape distinct polarization dynamics over time, with different implications for democratic debate.