What makes repository different from database, filesystem or any other kind of storage? How can I exactly tell that this or that is repository judging by some set of features that it has or does not have?
When I say 'repository', first of all I mean version control. But there are other examples of repositories, such as digital libraries, for instance. There might be other examples, of course, but all of them would assume that repository is 'the place where you can store something'. But it's not really clear what exact differences does it have that allows to distinct it from other 'places where you can store something'.
When I worked on repository software, many years ago. Back then, the difference between (general purpose) databases and repositories was the difference between "data" and "meta-data".
So, a database stores data. A repository is a special class of database which is designed to store meta-data, that is, data that describes other data.
Any general purpose database software could be used as a repository, but there are some characteristics of meta-data that make it desirable to use a special-purpose tool. Generally, the granularity of the data is small, with lots of cross-references to other data. The number of records is likely to be tractable. There is often a requirement for version control and/or diffs of the contents.
Because of these special requirements, database manufacturers were tempted into writing special DBMS systems to support the needs of repository builders. (Does anyone remember Microsoft Repository or the Unisys's UREP?) I am no longer in that field, and couldn't tell you about the progress in the past decade.