interference - Diffraction grating vs single slit

When I think about it, the single slit interference experiment should resemble the diffraction grating experiment as it is almost like single slit is the equivalent of a grating with many many many slits in a small length. So I would have though that the more slits you add in a diffraction grating, the closer its pattern of interference would resemble that of the single slit. However, it does not! The maximums become more and more distinct when adding more slits. Why do these two methods produce such different results? Thanks