To support inclusive and equitable study, higher educational institutions (HEIs) often address students categorised as 'disabled' in communications to provide information about support or encourage disclosure of information about conditions. However, if students do not identify with the language used it creates barriers to accessing support. There is little understanding of preferences and comfort with language in this area. This paper describes a study in a UK HEI developed to investigate language preferences for common points of communication with the HEI and level of comfort with particular statements. The outcomes of a prior study to elicit language models were used to develop a survey to capture views at scale from students with declared disabilities (n = 723). Terminology addressing students as 'disabled' was uncomfortable for many (particularly those with mental health conditions or specific learning difficulties, such as dyslexia). 'Additional study needs' was preferred. However, we find divergence in preferences across contexts, rather than a consistent preference for any recognised language model. We also identify clusters with significantly different perspectives on language within the population. This leads us to argue that differential and inclusive approaches should be explored, rather than solely focusing on a single model of appropriate language.