Microsoft Access is a well known database application, but it is not representative of the most common database system architecture. Most Access users perceive a database as a single file that can be opened by Microsoft Access.
The most common database system architecture is not file-based. Instead, it is server-client based. This means that a protocol is used to let a client send a request to a database server. When the database server completes the processing of the request, a reply is returned ot the client.
There are many advantages to this server-client approach. First of all, a single database can now be shared by a number of client (hosts). Secondly, a lot of high-end processing resources can be invested onto a single server host, and all clients can benefit from the investment. Last, but not least, this approach also removes the locality requirement. A client host that is physically remote from a database server can access its data just as easily as a client host that is on the same network as the database server.
MySQL is a commonly used database server on Linux-based platforms. For security, it supports SSL. Another well-known SQL server for Linux platforms is PostgreSQL.
Database serving tends to be more common with intranets. This is because the reply from a query to a database can be quite bulky. With SSL, the database query/reply traffic between two hosts is secure. As a result, security is not a reason why database serving is less common between Internet hosts.