Both these experiments have double slits but in one interference takes place and in the other both interference and diffraction. If diffraction takes place in double slit diffraction then it should also take place in Young's double slit experiment. How to explain the difference between the two?
Interference and diffraction are the same thing. In fact so is refraction.
The propagation of light is conveniently described using the Huygens-Fresnel principle. The amplitude of the EM wave at a point is calculated by summing up the amplitudes of all the EM waves reaching that point, taking the relative phases into account. This describes the phenomena we variously refer to as interference, diffraction and refraction. The separate names are largely an accident of history (and for convenience I suppose) - the underlying physical principle is the same.
YDSE is a special case of double slit diffraction.
In single slit experiment, it is known that if slit width d is smaller that wavelength λ, then we just see spreading of light with no fringe pattern. Then this slit acts a source of light. For two of such slits, you get two sources of light. Hence the superposition of two waves result in Interference pattern. This is YDSE
Now, consider the slit width to be greater than wavelength in single slit experiment. Here, you get a diffraction pattern on screen. For two of such slits, you will have diffraction in themselves and interference amongst each other. Hence you will get a hybrid kind of pattern whose involepe follows diffraction principle and the finer detail follows interference principle.
Diffraction is the phenomenon of the change of the movement from the straight line (in a flat, not curved space) in the cases, that it is not a reflection. For the expression "change of the movement from the straight line" it would be better to say "deflection", but this seems not to be so ok because, due to Wikipedia it could be misunderstood in every day life as a collision.
So a small ball inside a sharply bent pipe gets deflected or reflected (with very small angles) , but this is not a diffraction. Diffraction happens behind an edge. When the ball passes the end of the tube, it could spread out in different angles (if it was reflected inside the tube and if the start conditions are different for each thrown ball). So one get something like a diffraction. In the case of the balls this perhaps would be a normal distribution.
Interference is the periodically changing energy distribution along a line or area (the observation screen) of light behind slits or even every edge. For water waves one use a similar terminology. Diffraction is the change of movement of the maximum and minimum high of the water level behind edges, but not behind single edges. Interference is the periodically changing energy distribution along a line. For water waves this distribution stands never still, it moves.
Fig.: Interference of water waves behind two edges (a slit). The intensity distribution is a moving one, it does never stand still.