The local server is as if you are playing in single player mode, only that the clients (visitors) enter your server. This server allows the Host to host mods scripts or plugins that change the gameplay.

On the contrary, saying ♥♥♥♥♥♥♥♥ Dedicated Server, is only done by the developers (in the Valve case). And therefore you cannot use any mod scripts or plugins to modify the gameplay. Nor do you use some commands in the console, for example: kick, changelevel, z_difficulty, etc.

The only way you can use a dedicated server is to create a new one for yourself. It is complicated and I very much do not know how to create a dedicated server.

Here I leave you a guide on how to create a dedicated server and be able to use the mod admin system and some plugins.
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?l=spanish&id=276173458
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=764005219

Ok