What is the difference between database server, database and a database management system? Can we use any DB server for any DB?

You need to read books of the concerned subject for such basic information.

Well Let's put it this way. All your facts and figures is the data. The collection of data is database. Now if you want to search, add or update or delete any of the data u need to have a proper system/process to do the same. This system is ur database management system. Now DBMS' typically comes in a client server model. A server is something that provides u with services u ask for. Client is the one asking for the service.
Eg; U type URL in ur browser which is requesting for that web page. Now an appropriate server will respond and give you the page on your browser.

Similarly a DBMS' server is installed on Server hardware eg; IBM Server, HP server. Thus the DBMS' server side components(software) is installed and then u may access the databse from a client machine which has the DBMS' client side components installed.

Hope this solves ur query

Database server could be either oracle or sybase or informix. But the database , we create within these server for our purpose and this consists of all objects. DBMS is separate from these two, meaning how are you manging the data. using the row or col concept or in a file.
I hope i gave very clear picture and your answer. GOOD DAY