The European Union has proposed the Artificial Intelligence Act which introduces detailed requirements of transparency for AI systems. Many of these requirements can be addressed by the field of explainable AI (XAI), however, there is a fundamental difference between XAI and the Act regarding what transparency is. The Act views transparency as a means that supports wider values, such as accountability, human rights, and sustainable innovation. In contrast, XAI views transparency narrowly as an end in itself, focusing on explaining complex algorithmic properties without considering the socio-technical context. We call this difference the “transparency gap”. Failing to address the transparency gap, XAI risks leaving a range of transparency issues unaddressed. To begin to bridge this gap, we overview and clarify the terminology of how XAI and European regulation – the Act and the related General Data Protection Regulation (GDPR) – view basic definitions of transparency. By comparing the disparate views of XAI and regulation, we arrive at four axes where practical work could bridge the transparency gap: defining the scope of transparency, clarifying the legal status of XAI, addressing issues with conformity assessment, and building explainability for datasets.