Two different things, and on someone's profile you'll see a button for each: Add friend and Follow.
Following
Following means their posts appear in your feed. It's one-sided — they don't have to follow you back, and nothing is asked of them.
Friends
A friendship goes both ways and has to be accepted. Once you're friends you can message each other directly, without the message landing in a requests folder.
How the two interact
This is the part that surprises people:
Sending a friend request also follows them. The button becomes Requested, and you start seeing their posts straight away, before they've accepted anything.
Cancelling the request doesn't unfollow them. You stay following.
Unfriending doesn't unfollow them either. If you want out of both, do them separately — see Unfollowing Someone Without Unfriending Them.
When you're both friends and following, neither button is shown any more — there's nothing left to do.
Messaging
Being connected is what puts your message straight into someone's chats. Without it, your message goes to their Requests, and if they've set a price for incoming messages you'll be asked to pay it first. See How Chats Work on Sociala.
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