On Facebook and Instagram, there are options that let you share posts with select users (or Stories, in the case of Instagram). This means that while you can have a private profile, you can create posts that can only be seen by people you choose, or hidden from specific people that you choose.
Now it looks like Twitter is working on something similar codenamed “Flock” according to Alessandro Paluzzi. Basically with this Flock feature, which apparently won’t be the final name, users can create groups of up to 150 people to include in their “flock”. This means that when you post a tweet, you can choose to only have people in that group to see it.
So similar to what Facebook and Instagram are doing, this allows Twitter users to have public profiles but still post more personal things that maybe a random stranger on the internet won’t be able to see. Based on the way the feature is currently setup, Twitter says that users can add or remove people from this list anytime and they will not be notified, so if you have a falling out with one of your friends in your flock, you can remove them and they won’t know about it.
Right now, the only way for Twitter users to keep their tweets from being seen by strangers is to make their accounts private so that they get to choose who can follow them and who gets to see their tweets, so this “Flock” feature could help give users a bit more flexibility.