The term "directory" was actually already quite common for these kinds of systems (directory services) when AD came about, which is probably why it was called Active Directory. The Active bit was some kind of "en vogue" term for Microsoft back then, as mentioned ;)

It technically builts upon (amongst other systems) LDAP, the Lightweight Directory Access Protocol and X.500

I guess you could think of it more like a telephone directory - which again is also where the file system metaphor has its roots I guess. So the two are not so different in the end.