Numerous parties are calling for the democratisation of AI, but the phrase is used to refer to a variety of goals, the pursuit of which sometimes conflict. This paper identifies four kinds of AI democratisation that are commonly discussed: (1) the democratisation of AI use, (2) the democratisation of AI development, (3) the democratisation of AI profits, and (4) the democratisation of AI governance. Numerous goals and methods of achieving each form of democratisation are discussed. The main takeaway from this paper is that AI democratisation is a multifarious and sometimes conflicting concept that should not be conflated with improving AI accessibility. If we want to move beyond ambiguous commitments to democratising AI, to productive discussions of concrete policies and trade-offs, then we need to recognise the principal role of the democratisation of AI governance in navigating tradeoffs and risks across decisions around use, development, and profits.