Due to the architectural differences of the internals of those database managers (DB2, Oracle and SQL Server) some of those terms have slightly different definitions.
Then, let's try to start from the common ones:
- Database Stopped: when the Database Manager is stopped. The Database Manager is the actual Database Server, which services the connections the user make to the database. Then, when the database is stopped, the users can't access the database simply because it is not running. To stop the database, in normal conditions, you have to run some command specific to do that (like db2stop for DB2) or to stop the Windows service related to the database server you want to stop.
- Database network disconnection: this occurs when the network path between the client and the database server becomes unavailable, for any reason. If there are multiple clients to the database, and only the network connection of one client is broken down, then only the connections from that client are cut off - and the other clients do not suffer at all. The database client may be a workstation, an application server or even another database server.
However, if the network section which fails lies near the database server (for instance, the server's network card, cable, router or switch) then all the remote database client connections are broken too. On the other hand, even when the network outage occurs on the database server while the remote clients cannot access the database server anymore, the server isn't stopped. Then, if there are any connections coming from the database server (let's say the one of the application servers is installed in the same server of the database server) then those connections don't suffer any interruption. For the interrupted connections, all the database work done since the last database commit are lost (by an automatic database rollback).
- An Offline Database is simply when the database server isn't serving any connections - that can be because it is stopped or just because there aren't any users or applications trying to connect to it. However, in DB2 you can make a database online even without any connections to it, by issuing a "ACTIVATE DATABASE" command. That is possible because in DB2 you can have multiple databases being served by a single database manager instance. The database manager instance can be stopped or started is the program which manages the databases. In that case, the databases are where the CONNECT TO statements are issued to and have separated database transaction logs, bufferpools, tablespaces and tables for example. To offline a DB2 database, you can stop the database manager instance or deactivate the database you want to make offline.
I hope this can help you.