Tweets and retweets and quote tweets and replies and quote-tweet replies, oh my...

I created a Twitter recently. As part of this I'm getting to grips with all the different ways of interacting on there.

From what I can tell, your options are:

1. Tweets. These show up publicly on your account page. All of your followers will see these.
2. Replies. These appear publicly on the original tweet's page. Anyone who follows both you and the account you're replying to will see these. Anyone who follows only one of the two will not see this.
3. Retweets (RTs) and quote tweets (QTs). These show up publicly on your account page. All of your followers will see these. Retweets simply show up without comment; quote tweets show up like a normal tweet except they have the quoted tweet embedded at the end. There's a special button (the two arrows in a circle button, almost like ♻) for this. These are generally not meant for conversation.
4. DMs. Private. Archetypically one-to-one. May also allow group conversations? You can also share (embed?) tweets in this space just like the others.

From what I can tell, quote tweets are actually just "any tweet/reply you make with a link to another tweet at the end." The special UI for making tweets that quote other tweets is a convenience. Replies can also quote other tweets simply by including a link to another tweet at the end.

Specifically, on quoting a tweet in a reply: You create these by first (a) copying a link to another tweet, then (b) paste this link the end of your reply. (Thanks to Ayal Telem's Quora answer.)

Elaborating on this a bit from what I understand:

1. Replies are a semi-public space. Anyone can find them — but they are not spread as widely as regular tweets, retweets, quote tweets.
2. Quote tweets are broadcast responses — unlike replies which are directed at the original tweet's account.
3. Replies are conventionally used to start or continue a semi-public conversation. Quote tweets are not.
4. All kinds of responses — replies, retweets and quote tweets — notify the author account.

Links

1. https://help.twitter.com/en/using-twitter#tweets
2. https://www.quora.com/How-do-I-quote-someones-tweet-while-replying-to-another-tweet/answer/Ayal-Telem
3. https://www.itgeared.com/how-to-quote-tweet-in-a-reply/
4. https://www.wikihow.com/Quote-a-Tweet
5. https://beastoftraal.com/2021/06/10/a-reply-vs-a-quote-tweet-quote-post-should-you-react/
6. https://members.tinshingle.com/content/what-quote-tweet-and-when-do-i-want-use-it-instead-retweet