I have a doubt with the concept of server and client in the database.I am developing an application which needs a centralized server for holding the updated information from which all the clients would be getting it.And also the other way updation also should work where information is sent from the client to the server.

When it comes to the actual implementation I have a doubt if there are two separate kind of databases I am going to install-one on server and one on PCs or is it that both are same and just the way we look at them are different.

I am using Sqlite as of now on the client Pcs, is there a server application of sqlite?

If you install a SQL server product, whether you install it on a server or client operating system, it is still functioning as a "server" role. Server in this capacitiy means that it will be servicing clients (or consumers). This has nothing to do with regard to which operating system you run it on.

For example, with a typical web / database implmentation, you have a back-end SQL system (this would be considered the SQL server) and you would have a front-end client that makes SQL requests (this would be the web server).