This study leverages mobile data for 5.4 million users to unveil the complex dynamics of daily mobility and longer-term relocations in and from Santiago, Chile, during the COVID-19 pandemic, focusing on socioeconomic differentials. We estimated a relative increase in daily mobility, in 2020, for lower-income compared to higher-income regions. In contrast, longer-term relocation rose primarily among higher-income groups. These shifts indicate nuanced responses to the pandemic across socioeconomic classes. Compared to 2017, economic factors in 2020 had a stronger influence on the decision to relocate and the selection of destinations, suggesting transformations in mobility behaviors. Contrary to previously held beliefs, there was no evidence supporting a preference for rural over urban destinations, despite the surge in emigration from Santiago during the pandemic. This study enhances our understanding of how varying socioeconomic conditions interact with mobility decisions during crises and provides insights for policymakers aiming to enact fair and evidence-based measures in rapidly changing circumstances.