These are related but not exactly the same. ``Interference'' is the more general concept: it refers to the phenemenon of waves interacting. Waves will add constructively or destructively according to their phase difference. ``Diffraction'' usually refers to the spreading wave pattern from a finite-width aperture. The resulting pattern can be considered as due to the interference of many point sources along the aperture. If you have infinitely-narrow slits, there will be just interference, but for finite-width slits there can be both interference and diffraction effects (like in your lab).