Nastic movements - These are nondirectional movements which takes place in living parts of plant due to the stimulus like temperature, amount of water etc.
For example - Whenever there is excess amount of water stomata open. This is a nondirectional movement which takes place due to presence of excess water.
Curvature movements - These are directional movements which take place due to stimulus like light, some chemicals etc.
For example - Shoot of a plant moves toward the direction of light. Here the movement is directional due to presence of light in a particular direction.