Trust features prominently in a number of policy documents that have been issued in recent years to facilitate data sharing and international collaboration in medical research. However, it often remains unclear what is meant by 'trust'. By exploring a concrete international collaboration between Denmark and Pakistan, we develop a way of unpacking trust that shifts focus from what trust 'is' to what people invest in relationships and what references to trust do for them in these relationships. Based on interviews in both Pakistan and Denmark with people who provide blood samples and health data for the same laboratory, we find that when participants discuss trust they are trying to shape their relationship to researchers while simultaneously communicating important hopes, fears and expectations. The types of trust people talk about are never unconditional, but involve awareness of uncertainties and risks. There are different things at stake for people in different contexts, and therefore it is not the same to trust researchers in Pakistan as it is in Denmark, even when participants donate to the same laboratory. We conclude that casual references to 'trust' in policy documents risk glossing over important local differences and contribute to a de-politicization of basic inequalities in access to healthcare.