On Mastodon, there are two ways of labelling posts: Favourites and Bookmarks.
Here's a quick comparison...
You can add a Favourite by clicking the star ⭐ below a post.
Favourites are pretty much just likes, and the person who wrote the post will get a notification when you add a favourite. Other people who can see the post will also be able to see who favourited it.
You can see all your past favourites by logging in through the website and clicking "Favourites".
You can add a Bookmark by clicking the bookmark 🔖 below a post, or if it isn't visible click ⋯ and then select "Bookmark".
Bookmarks are much more private, only you can see which posts you've bookmarked. No one gets any notifications when you add a bookmark.
You can see all your past Bookmarks by logging in through the website and clicking "Bookmarks".
Note that the official Mastodon app doesn't have bookmark support yet. You will have to use the website or a third party app.
@feditips
That's a nice hint. I always used favorites as bookmarks.
Now you got less "likes" for your posts, but more bookmarks. At least from me, because I completely changed my logic.
@aircan
If you're bookmarking my posts, they are all available on https://fedi.tips too :)
(The website version actually has expanded tips as there are no character limits!)