@Aslak No, the Game and the Server don't have to be identical.
But they, of course, should both have the Content installed that you want to use on the Server.

BTW Do you use DLC Content now?
To join the Server over a LAN Shortcut, do this:
Go to the Folder
..\rFactor 2\Launcher
and make a Rightclick with the Mouse on the
Launch rFactor.exe and select "create Shortcut"
Then rightclick on the new created Shortcut and select Properties.
Enter the following into the Field "Target:"
"G:\Steam\steamapps\common\rFactor 2\Launcher\Launch rFactor.exe" +multiplayer +connect="127.0.0.1:64297"
or, if you use a Password:
"G:\Steam\steamapps\common\rFactor 2\Launcher\Launch rFactor.exe" +multiplayer +connect="127.0.0.1:64297" +password YOUR_PASSWORD
(there must be a Space between +password and YOUR_PASSWORD)
And enter this into the Field "execute in:"
"G:\Steam\steamapps\common\rFactor 2\Launcher"
You of course have to replace the shown Path
G:\Steam\steamapps\common\rFactor 2 with your Path
and if you use another Port than 64297, you have to replace that too.
The IP has to stay as it is.
If everything is done, click OK to save the Shortcut.
Then shut down the Steam Client and start the Steam dedicated Server first.
When it is running, doubleclick on the new created Shortcut.
You should join the Server now.