No, these are special programs just for viewing Twitter, with a different interface, or special features that most users wouldn't need. There was one, I think it was TweetDeck, that was particularly popular with celebrities because it could be set up in a way to cope with the large number of tweets directed at them compared to the average schmo. Mastodon, in contrast, is a totally separate service, which also has third party apps that do the same thing (and it looks like it's about to have a lot more, since several were just forced off of Twitter and those developers have to develop something).
Twitter has always had a fraught relationship with third-party clients. A while ago, they restricted the API quite a bit in hopes of forcing people to use their website or the official app. For instance, I guess it must have been rolled back because I never heard of it actually applying, but at one point they set a limit for the number of access tokens any third-party app or service could be assigned, so if any app got over a certain number of uses, they'd just have to stop letting new people use it. Oddly enough, while third-party apps don't show ads or promoted tweets, so don't directly make Twitter any money, that's Twitter's doing, they could easily put the ads into the data sources the apps draw on.
Tech writer Jason Snell has suggested a couple times recently that, since Twitter is always so hard-up for money, they should've made third-party app access a paid feature years ago. The people who use Twitter apps are one kind of power-user or another, they're the ones who care enough about their experience to go out looking for a way to make it better, they'd pay a fee to not have to use the website interface or Twitter's own app, either because they need the special features of other apps, or they just like it better and use twitter enough to make a difference. That's also the exact reason why this move is penny-wise and pound-foolish. Musk probably realized all these people using TweetDeck and TweetBot and Twitterific and whatever weren't making him any money because they don't see ads, and they don't get the weird promoted algorithmic timeline where you see everything but the tweets posted by the people you follow, but they probably disproportionately post and share most of the tweets that the silent majority of casual users who do use the website or Twitter's own app are interested in. It's the same exact thing he did when he first started, when he seemed completely baffled by Stephen King quipping that Twitter should be paying him to be on the site, not the other way around.
ing ad revenue, will it? 
