This paper takes on one of the rarely articulated yet important questions pertaining to digital media objects: how do HCI and design researchers understand 'gifting' when the object can just as easily be 'shared'? This question has often been implied and occasionally answered, though only partially. We propose the concept of 'inalienability', taken from the gifting literature, as a useful theory for clarifying what design researchers mean by gifting in a digital context. We apply 'inalienability' to three papers from the ACM Digital Library and one ongoing project, spanning nearly two decades of HCI and design research, that combine 'gifting and 'shar-ing' in their frameworks. In this way we show how applying the concept of 'inalienability' can clarify behaviours that mark gifting as a unique activity, frame research questions around gifting and sharing, outline specific next steps for gifting research, and suggest design strategies in this area.