Once you detach your database there will not be an entry in the sysdatabases system table.
i.e you can query and confirm the same as
Select * from master..sysdatabases
In the end result of the above query you cannot see the db you have detached whereas
if you bring the database offline, there will be an entry present in the sysdatabases system table;
You can verify the same by running the above query and you can see that the db you took OFFLINE will be present in the sysdatabases table !
Basically, detaching/attaching is used to move database files between instances(servers) where as in Offline you can not move files. After detaching, the database will be removed from SQL Server but will be intact within the data and transaction log files that compose the database. The purpose of these commands are totally different though it looks like same.