There are three main timelines on here:

🏠 Home - Posts from people you follow, plus posts featuring hashtags you follow

πŸ‘₯ Local - Public posts from people on your server

🌎 Federated - Public posts from people on any server

On the official Mastodon app, Local is known as "Community" and can be accessed by clicking the magnifying glass πŸ” and scrolling across to the Community tab.

There are no algorithms hiding or moving stuff. You see all the posts for each feed in chronological order.

@feditips does each mastodon (or other app) instance have it’s own database?

@thatscrazy each mastodon (or fediverse software) instance does has it's own database, for that instance.

it's required for keeping track of users on your instance.