What is the clear difference between interference and diffraction? Richard Feynman said in his book.

"No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do is, roughly speaking, is to say that when there are only a few sources, say two interfering sources, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used."

Is there a more clear distinction between the two, interference and diffraction?
 A: I didn't know this Feynman's quote, and to be honest it worries me a bit, because I didn't feel that there was a problem here, but Feynman usually was right!
Here's, however, how I usually explain this to my students, usually during and after both quantum physics and optics lessons.
Although it appears in classical physics, diffraction is a consequence of Heisenberg's inequality. As you limit the transverse spatial dispersion of a wave (force it to go through a hole), its tranverse momentum dispersion explodes, changing the shape of the wave front.
This happens with any wave. It's been a game in quantum physics for 20 years to see who could make larger and larger molecules diffract.
Interference happens when two waves meet while satisfying some coherence conditions. Then their amplitudes add up, but not their intensity (intensity being defined differently, depending on the sort of wave: energy for electromagnetic waves, probability for quantum waves).
We've known for (roughly) the past 40 years that a single wave can interfere with itself, for example when its wave front is split and rejoined later (that's a typical situation where diffraction and interference both happen).
The last part of Feynman's quote puzzles me a bit. I think he was refering to a grating. The way I see it, each slit/hole in the grating diffracts the incoming light, generating as many coherent waves, and those waves interfere further down their path. In my optics lesson about diffraction grating, I in fact spend most of the time doing interference computations, and not that much diffraction.
Perhaps vocabulary has evolved since Feynman said that, I don't know.
A: Feynman was likely referring specifically to the DSE/light and not waves in general.  Diffraction and "interference" are clearly distinct.
Water waves going thru a single slit DO diffract (spread out per Huygens) but do NOT interfere (there is a common misconception that they do). Diffraction is the spreading out of wave fronts.
Interference is very unique and is the bright and dark bands observed in the DSE or the patterns observed in water waves for example.
For the DSE the term interference pattern and diffraction pattern has been used interchangeably for a long time.
A: From Wikipedia article on Diffraction:

Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening.

Interference might happen in more general conditions, even between the light emitted from different sources. Thus, it is fair to say that while diffraction implies interference, one may have interference without diffraction.
As for the Feynmann quote - I think it applies to a specific context, rather than to diffraction in general. Also, even big scientists (or perhaps especially big scientists) sometimes have their idiosyncratic definitions, which do not pose any problem to anyone, as long as one defines clearly what is meant, before launching into a discussion.
A: Although diffraction and interference are mostly referred to phenomena of light, I would like to start with water waves.
The problem is best observed at the surface between water and air. In a water channel with vertical walls, a plane water wave travels almost undisturbed. A plane wave is not weakened by lateral propagation at the ends of the wave. We see a pure transverse wave in which there is a pure upward and downward movement of the water molecules along with density changes.
As soon as the channel becomes abruptly wider, the wave ends on the left and right will diverge in a circular pattern, with their amplitude weakening.
If the experiment changes so that the channel becomes a slit, you still have the same result. What is decisive is not what happens in front of the slit to the right and left of it - this part of the wave is simply reflected - but what happens after the slit in the previously calm water - the wave spreads out in a circle to the left and right of the slit. This phenomenon is called diffraction of water waves.
When two water waves meet, their amplitudes can strengthen (the molecules move in the same direction at that point and time) or weaken. This phenomenon is called interference of water waves.

Things happen a little differently with particle streams. It is irrelevant whether we are dealing with electromagnetic radiation or electrons.
Even when two currents meet head-on, nothing usually happens. However, when the intensity of the currents increases, particles can collide. The electrons then change their direction, they are scattered.
This behaviour does not change when the particle currents are emitted in waves, i.e. for EM radiation as a radio wave. The waves penetrate each other effortlessly. Since information is usually imprinted on such waves, the two pieces of information may overlap in the case of a receiver. However, this is by no means interference in our sense.
This also makes it clear that the term interference for particle streams behind edges is only a common name. In reality, however, it is a matter of deflections aka diffraction of the particles at the edges and an intensity distribution behind the edges.
