"Start server" is for locally hosted temporary servers. If the host goes offline, so does the server. "Community servers" are persistent servers that are always online regardless if the server owner is or not.

For example, when I click 'start server', I'm actually hosting the game off my PC. Other players can only connect to me while I'm playing, and the server session ends the moment I quit the game.

For the community server that I run, I'm renting a shard from a server provider that hosts the game for me. Players can connect to my server at any time as long as the server is online.