What is the difference between diffraction and interference?

Diffraction is the bending of waves around an obstacle, whereas interference is the meeting of two waves. For example, diffraction is what results from a pinhole blocking a wave source; the wave spreads out from that one point. This effect is what makes shadows, regions where the light source is blocked but it is not completely dark. Interference, though, results from two waves colliding with one another undergoing constructive and destructive interference, as in two chords being played. I think the confusion concerning these two dissimilar phenomena is the fact that two pinholes, two diffraction sources, results in interference of two sources, which is what the diffraction grating is, which makes the characteristic bands of light and dark interference patterns.