How can I keep two tables in two different databases with different schemas the same in real-time?
As there are two servers there are no real good options. Pretty much your only choice will be to use triggers in both databases that write to the remote database. You'll need logic in the trigger so that the trigger does nothing if the call is coming from the other SQL instance. Otherwise you'll end up with a deadlock every time. 

If one instance is down than nothing will work until that server is back up and running.