The difference between the connect function to the follow function is like how it works on Facebook. You would send a friend request (connection request) if you want to be friends with someone, then hit the follow button if you would just like to be updated on a certain user's activity.
The connection is more powerful than the following feature, only the connected users are allowed to message each other while the followers would not able to message if you are not connected.
The Connections Setting needs to be configured for this to work. Go to BuddyBoss > Settings > Connections > Messaging: Require non-admin members to be connected before they can message each other.