There seems to be a general confusion about what Access is. probably about what a database is, as well. A database consists of a bunch of files which are created by sending commands to database engine. It may also have a front end that makes it easier to send the commands and view the results of these commands. These are commonly thought of collectively as "the database" but they're at least conceptually independant, if not functionally. It's not dissimilar to how your PC runs: application software on an operating system on hardware. You tell you application what to do; it tells your OS; your OS tells your hardware.
Access basically a front end. It has a bunch of tools and so forth built into it, but it is not really a database. It's not even a database engine (it uses the JET database engine, as I recall). You use Access to create a database - which it does by sending commands to the database engine which processes them and (if necessary) records them in the MDB file. There are other tools that can be used to access the MDB files; Access is merely the simplest and most convienient. Similarly, Access can be used to manipulate other database engines (eg it can be used as a front-end for SQL Server).
For the record, MYSQL is primarily a database engine.