Most early Institutional Repositories were research repositories. Some are purely repositories housing digital objects as in "Repositories are "collections of digital objects"". However, since one of the primary aims is to showcase the intellectual assets of the institutions (as compared to providing Open Access to peer reviewed journal articles) another model was 'hybrid'. The use as a bibliography (suggested both by previous practice and by senior academics) required the metadata to be deposited even if it was not possible to deposit the 'publication'. This is particularly important if you want to showcase well the whole institution, including the Humanities, where outputs are not so easily deposited eg a book or exhibition.
Therefore one model is 'hybrid' including both digital objects and their metadata and sometimes just metadata or metadata plus links to trusted repositories elsewhere. This latter aspect may become more important as the number of these trusted (eg funder) repositories grow. Of course, you can also make a subset of this repository which includes 'full text only' as in the alternative " digital object repository" model but this does not then give a full picture of the institution.
Hey, Jessie M.N., Simpson, Pauline and Carr, Leslie A. (2005) The TARDis Route Map to Open Access: developing an Institutional Repository Model. In, Dobreva, Milena and Engelen, Jan (eds.) ELPUB2005 From Author to Reader: Challenges for the Digital Content Chain: Proceedings of the 9th ICCC International Conference on Electronic Publishing, Katholieke Universiteit Leuven, Leuven-Heverlee, Belgium, 8-10 June 2005. Leuven, Belgium, Peeters Publishing, 179-182.