Yes, the terminology is very inconsistent. The most consistent way to handle it would probably be to declare that birth is a "fact type" and that John Doe's birth is an "event". Hence, in a consistent genealogy software world there would be "fact types" and "events", but no "facts". But we human beings are not consistent, and we can easily identify "facts" as being the same as "fact types" in one instant and we can easily identify "facts" as being the same as "events" in another instant. We users do it, and it seems that the RM developers also do it.
To further elaborate on Laura's excellent discussion of tagging media in this thread, there are two very confusing aspects of the user interface. One of these confusing aspects is the ability that I mentioned earlier in the thread to start with an object in RM such as a birth event or a citation for a birth event and connect to a media file via Add New Media or Add From Gallery, or alternatively to start with a media file and to tag the media file to an object in RM such as a birth event or a citation to a birth event. I wouldn't want to remove either capability, but the fact that you can do it in either direction can make it very confusing.
Even more confusing, I think, is that no matter in which direction you do the connecting, media files can be connected to a birth event or to a source for a birth event or to a citation for a birth event (and the same for any other type of event). It's a common question from beginners (and sometimes from experienced users) as to where is the best place to do such connecting of media files - to an event itself or to a source or citation for an event.
It seems to me that the most logical place to attach a media file as documentation is to attach the file either to a source for an event or to a citation for an event. Of these two choices, which makes more sense has a great deal to do with whether you are a so-called lumper or splitter of sources and citations. But there are idiosyncrasies in the user interface that can lead you to attach documentation to the event rather than to a source or citation for an event.
If you are at a media file and are tagging it to something, it's just as easy to tag the file to a source or citation for an event as it is to tag the file to an event itself. In this case, I don't think the user interface leads you astray and my personal recommendation is certainly to tag a media file which is documentation either to a source or to a citation.
If you are at an event and connecting in a media file as documentation via Add New Media or Add From Gallery, it's much easier to connect the media file to the event itself. The place to put the connection is very visible in the user interface, and the user interface pulls you very much in the direction connecting the media file to the event. In order to connect the media file to a source or citation for the event in this situation, you have to drill down very deeply into the user interface and it can be very difficult to find the proper place to establish the connection. Indeed, even if you have previously placed the connection to a media file at the level in the user interface of a source or citation for an event, it can be very difficult to find the connection again. So for example, you might establish the connection by tagging from the media file in the Media Gallery, and then find it very difficult to find the connection in the Edit Person screen. Until and unless the user interface is changed to address this issue, it's going to be a problem for a lot of users.