I’ll do my best to explain both below:
The “Suppressed from latest” feature is essentially a forced global mute for a specific category. The category still appears as it normally would on the Categories page, but topics from suppressed categories do not appear on the Latest page. It effectively takes away the user’s power to customize some of their experience on the Latest page. Some community managers find this behavior helpful under specific circumstances. The feature was split out into a plugin: https://github.com/discourse/discourse-categories-suppressed
With muting, you can mute topics, tags, categories, and even users. Each context is a little different, though:
- Topic: You will never be notified of anything about the topic, and it will not appear in latest.
-
Tag: You will not be notified of anything about new topics with the tag, and they will not appear on your unread tab. (Note that there is a
remove muted tags from latestsite setting to tweak muted tag behavior). - Category: You will never be notified of anything about new topics in the category, and they will not appear in latest. Muted categories are placed at the end of the category list on the Categories page and appear much less prominently.
- Users: Suppress all posts, notifications, and PMs from a user
As an admin, you can set default muted tags and categories from your site settings. However, users will always be able to override the defaults from their user preferences.
There is also a mute all categories by default site setting that creates an opt-in experience for users.