Vibration is the periodic motion and the restoring force is the Force due to elastic property of body. Rigid body can not vibrate. Anything has mass and elasticity can vibrate.
Oscillation is also Periodic motion and restoring force is due to weight of the body. even rigid body can oscillate.
String of violin is in motion due potential energy gained by change in length of the string, i.e. due to elastic property of the body. So motion is vibratory motion. also periodic motion.
body not moving in straight line or circular path so no linear motion or circulatory motion.