The upsurge of policies and guidelines that aim to ensure Artificial Intelligence (AI) systems are safe and trustworthy has led to a fragmented landscape of AI governance. The European Union (EU) is a key actor in the development of such policies and guidelines. Its High-Level Expert Group (HLEG) issued an influential set of guidelines for trustworthy AI, followed in 2024 by the adoption of the EU AI Act. While the EU policies and guidelines are expected to be aligned, they may differ in their scope, areas of emphasis, degrees of normativity, and priorities in relation to AI. To gain a broad understanding of AI governance from the EU perspective, we leverage qualitative thematic analysis approaches to uncover prevalent themes in key EU documents, including the AI Act and the HLEG Ethics Guidelines. We further employ quantitative topic modelling approaches, specifically through the use of the BERTopic model, to enhance the results and increase the document sample to include EU AI policy documents published post-2018. We present a novel perspective on EU policies, tracking the evolution of its approach to addressing AI governance.