For oscillator, you only supply voltage then oscillator can generate frequency.
But for crystal, crystal is part of oscillator same as suru told. Actually we can image crystal like R, L and C series connection. And if you connect with oscillation circuit, it will generate frequency at resonance point.
any oscillator consist of few part:1-tune circuit wich by this part we tune value of oscillationfrequency
2-amplifire
3-feedback
crystal just is a tune circuit.
Crystal is a rasonator which you can use it to function as a rasonance filter in the circuit. And if you have some positive feedback of the rasonanced frequency it will oscillate which is a oscillator.