Instagram is currently working on a user function which aids its users in sharing is contents to any specified person or group, termed favourites. You don’t expect Instagram to fold it hands in face of the fierce competition from Snapchat and all the other guys.
For sure this is a friend list in an unusual way as it is intended for only one person or group to participate thereby making it very unique and different from its parent model or even twitter.
With this feature, the right to share to whoever you please are strictly yours, whether be it a normal post or a story post. Once favourites is selected, only those people in that list gets to see your post which will be indicated by a green badge.
On your profile, a star representing your favourite tab will keep all your posts you have shared with your favourites. On this favourite tab, there is no restriction to the number of persons or groups you can add or subtract. You can freely control these without annoying those who you intend to remove as those removed don’t get notified.
Nonetheless, if they are removed from your favourites, they cannot see your private posts any more.
You get to know you are on someone’s favourites lists as there will be a green badge at the top of the posts shared with you.