Worker
UK employment law has three statuses, not two: employee, worker, and genuinely self-employed. Worker sits in the middle and is the one charities meet unexpectedly, usually because a volunteer arrangement drifted into something more contractual.
Status is determined by the reality of the arrangement, not by the label on the paperwork. A tribunal looks at whether there is an obligation to provide work and to perform it personally, and at how much control the organisation exercises. Calling someone a volunteer or a contractor does not settle the question.
If you are paying anyone anything beyond expenses, or expecting them to turn up on a rota, check the status before it is decided for you. See employment status, and the free ACAS helpline for a specific case.