maybe you are referring to the 'Listed'. It's only the owner's way of categorizing his or her followers. but it's all until there.
When it comes to Twitter groups, you’re probably either interested in ways to communicate with a distinct set of users, or following a group of tweets based on Twitterer, topic, or hashtag. We’ve identified and separated out the web, desktop, and mobile apps that help you satisfy the group function of your choosing.
Are you really pertaining to groups on twitter or groups on facebook? because i don't think there is such thing as twitter groups.
hey.. may be mikeleonard is talking about lists which for smb seem as groups. Those groups are compiled by other users. They add to their lists, so to have separate twitter feed for people who have smth in common!
There is no group in twitter. The people that you followed are already your group. All you need to do is have the right article to post on twitter in order for people that you want to get a good feedback reply to you or send you a personal message.