Public Trackers could include something like yifi or 1337x. Although I'm not sure if jackett provides any pre-configuration of those. And for private you can for now, unfortunately, keep an watch on r/opensignups (sometimes they let anyone sign up). Or you can join the interviews for Myanonamouse and Redacted. The first one is related to books and the second one is related to music. But once you join them and climb through the userclasses, they have invite threads for other reputed private trackers.
edgerunnergit
There are two kinds of torrent sites: public and private. Private torrent sites require you to be a member of the site, and only then are you able to download any content. Private sites also may have a whole bunch of seeding, downloading, uploading rules in action. So you cannot just download something and remove that from your client after download is complete. Such sites often require interviews or invitations from existing members.
Now in Jackett, you can add both public torrent trackers and private torrent trackers (if you are a part of them). Each site may provide their own API key or sometimes just username/password, or sometimes nothing for public trackers.
Edit: It could also include usenet indexers.
TL;DR: Indexers are torrent sites (public and private) that you add to your jackett with either API keys or username/password or nothing in cases of public sites.
Lemmy know if something better comes along