Fear is an emotion and a response to a perceived threat. It may be that the threat proves to be something harmless, like the shadowy shape in the dark room that's actually a chair with a coat thrown on top of it. Or it may be a genuine threat and the fear is a good response for survival -- in spite of what Yoda says, sometimes fear is beneficial for us.
Adoption, on the other hand, is the way something or someone is brought into an already-existing group. The most common picture of it for us is the legal process that a family uses to bring in a child who was born to other parents, but we also use it to talk about how we might begin a new practice or accept a new idea.
I think Paul may be comparing them here in the context of obedience. Obedience out of fear of the consequences of disobedience is the most basic level, the one we learn as kids when we don't really understand the concepts. I'm told not to touch the stove because it's hot, I touch it, I get burned and now I obey when I'm told not to touch something hot.
But obedience from fear is not ideal. For one, there can come a point when the consequences of disobedience seem less of a burden than continuing to obey. This is the thought behind revolutions and rebellions: If we defy authority, bad things may happen. But we can no longer continue to live under this authority, whatever it is. And so the threat the authority makes no longer has power, and a man will stand in front of a column of tanks and make them stop.
And from the point of view of those kept in check by fear, there is no peace in that way of living. We may have a list of rules we have to follow in order to make sure we stay in line, but what happens when we run into something the rules don't cover? If we act, we may act the wrong way and suffer the consequences. A faith life based in fear offers no peace and no rest either. We worry that God is just waiting for us to take one step wrong so he can get his Zeus on and thunderbolt us to oblivion.
This way of thinking makes obedience the prerequisite for a relationship with God, and yet when we read the gospel and what Paul says about it we see pretty clearly spelled out that we can never "obey our way" into the kingdom of God.
A spirit of adoption, though, brings a whole new dimension to our understanding of obedience and even a whole new level of power to help us live as God asks us to live. With this spirit, the Godly life comes as a show of praise and thanksgiving to the one who saved and healed us of the consequences of our sin. Obedience itself is a consequence of God's actions in our lives and a desire to live according to our new family and community. In the same way that a child adopted when he or she is older has to unlearn old family systems and learn new ones, we now want to unlearn our old ways of life in exchange for God's ways.
We have become a part of a new family and we want to make sure that there is a strong family resemblance.