"Add new post" basically posts a microblog to federated microblogging sites like mastodon from Kbin using your Kbin account. These are presented under the microblog category of the magazine you posted in. "Add new thread", formerly "Add new article" is what gets your post under the threads category.
If an owner of a magazine adds tags to their magazine, the microblog section of that magazine starts aggregating microblog posts from across the fediverse that use those tags.
If you are trying to post a Kbin magazine "thread" from mastodon, I don't think that's possible, as mastodon is exclusively a microblogging site. Adding a tag to your post that's included in a Kbin magazine should get your post to appear in its microblog section, though. Maybe mentioning it as well, I'm not sure.
If you want a Kbin magazine thread to appear as a microblog post on mastodon, I'm not sure that's possible. I've never tried it. Maybe adding a tag could do something, but I doubt it.
Not sure if this helps at all, but good luck.