Can somebody explain to me what is the difference between double slit diffraction and double slit interference?, to me they are the same thing but my teacher says they have two different meanings, thanks.
In that diagram, the dotted line is the same shape pattern that you would get if only one of the two slits were open. It's often called the "diffraction" part of the pattern because it's the same as single-slit diffraction. The rapid variation of the actual pattern (the solid line) is often called the "interference" part of the pattern, because it's caused by interference between the two slits.
Both parts of the pattern are caused by interference: the "diffraction" part comes from interference between light waves from different parts of the same slit, whereas the "interference" part comes from interference between waves from different slits.