If you're fearful, you're afraid of something. A kid who's fearful around dogs might cry or run away when sees even a small puppy.
To be fearful is, literally, to be full of fear. You can also use this adjective to describe the thing that scares you: "I lay awake all night listening to the fearful creaks of the old house around me." Some people are always fearful — it's just part of who they are — while others are only fearful in certain instances. You might be fearful on airplanes but fearless when riding a horse.