A centralized database system is the traditional database schema in which the database at located in one place. It is not to say the database may not be distributed among several servers, mind you. It simply means the database is considered one unit managed by one DBMS in one location and to which clients connect.
A distributed database configuration is achieved when there are several database servers replicating (or not) information between themselves and each with its own DBMS to which clients connect. Many companies starting at a given size now operate in this model. Branches or small offices hold their own - usually - stripped down version of the main database and data is usually replicated through scheduling.
Mind you that it is irrelevant how these databases are connected. WAN, LAN, Internet, is all the same.
I have no idea what a client-server database configuration is. Only thing I can think of is the client being some sort of filter through which requests to and from the database are passed. In that sense, users would connect to the client and not directly to the DBMS.
