If you look at the Gospels, you'll notice several times when Jesus was preaching and drew a crowd, then separated Himself from the crowd somehow, and only a few people followed Him. Once or twice He went up a hill, and a handful followed Him. Once he went across a lake, and a few followed Him. In essence, I think the main difference is the level of commitment.
The book, "Experiencing Spritual Breakthroughs" speaks of 1st, 2nd, and 3rd chair Christians. It describes 1st chair Christians as fully devoted followers of Jesus. These are people who have given their lives to Jesus and are walking with Him 24/7. These I would consider 'disciples'.
As the book describes them, 2nd chair Christians are what I call "Sunday Morning Christians". These people are in church every Sunday, and know everyone there, but as soon as Monday rolls around, they revert back to their own way. These might be what I would consider 'followers'.
The reason, I think, Jesus wants us to be 'disciples' is because discipleship is where His blessings are abundant, and our lives are lived to the fullest--just as He intended (John 10:10).