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 gets opened. 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.