A Loop has a definite probability. I go back, stop my grandfather from dying, this makes something worse happen, so someone goes forward in time and stops me. A small loop in time is made from a defined origin, but it can exist.
A Paradox is different because it can't exist. Ex: I get a ball from someone in the past. This is the first time I ever got the ball. I go back, and give him the ball, and thats how he received it for the first time. Where did the ball come from? It has no defined origin and cannot exist.
Ultimecia giving her powers to Edea doesn't prove anything, other then the developers wanted to add something interesting in, but created a large paradox.
