The rise of generative AI (GenAI) chatbots accessible via conversational interfaces is transforming digital interactions and holds economic promise. However, these tools might deepen existing inequalities -- not only through uneven, socially stratified adoption, but through differentials in their purposeful, critical use. Drawing on original survey data from 1,906 Italian-speaking adults, we provide a comprehensive analysis of GenAI adoption, literacy, and usage patterns. Our findings show that GenAI is supporting diversified personal and professional activities and replacing traditional information-seeking tools. Yet less-educated and older individuals, and those with lower technology familiarity, are less likely to adopt it; 40% cite competence barriers as a key obstacle. Among users, AI training emerges as the primary predictor of purposeful, capital-enhancing engagement -- content creation, learning, and creativity enhancement -- while more passive, recreational uses (e.g., companionship, information seeking) remain insensitive to competence levels. We thus highlight digital literacy as a lever for how people leverage GenAI, not just whether they use it. Finally, gender operates as a persistent cross-cutting divide, shaping both adoption and usage frequency. These findings challenge the assumption that high accessibility translates into broadly shared gains. Rather, they offer a granular, multi-level account of emerging disparities in the GenAI era -- with implications for how this technology may ultimately drive outcomes and benefit divides.