Is there a difference between a diffraction pattern and an interference pattern? I am in high school at the moment and I am revising a section on waves. I am slightly confused by some things in our notes, which I would like to ask about.
We looked at Young’s double slit experiment, and the following is my understanding:
Both slits diffract the incident light, forming ‘semi-circle’ wavefronts. Where the two semicircles (one from each slit) intersect, they can interfere, forming a disturbance pattern on a screen placed there.
We then looked at diffraction grating, and I initially thought that the same thing was occurring there, only with far more semicircles. My professor, however, explained something different. He said that although the same kind of interference does happen,  it is hard to see, and that the main fringes could only be seen with a lens. He then showed how parallel light rays could be focused, and then would either form a bright fringe or a dark fringe, depending on whether the path distance was an integer or half-integer wavelength apart.
My professor said that, at our level, there is a kind of distinction between interference fringes (like what is happening in Young’s experiment), and diffraction fringes (like with the ‘main part’ of diffraction grating).
I can’t seem to understand the difference, and especially what determines which of the two is the dominant one in any given experiment. I hope I have made myself clear, because I find it very difficult to explain my confusion - feel free to ask for any clarification, and thank you very much for your answers, it means a lot.
 A: You're not alone.
It's easy to give a definition of interference.  It's the consequence of the superposition of field amplitude.  Sometimes they add, sometimes they subtract.
The word diffraction causes problems because it does not admit an easy, one-sentence definition.   In part, this is due to sloppy usage of the two words.   A working definition that works most of the time is "the phenomenon of light changing direction on account of an obstacle of some kind in the path of the light."
A laser produces a narrow beam of light. A laser pointed at an object far away produces a small circle of light.  How far is "far"?  If you looked at the spot formed on different objects nearby, the spot stays the same size as the distance to the object grows.  If you look at objects farther away you will find that the spot gets larger and larger the farther away you get.  If I look far enough away, we find that the size of the spot varies linearly with distance from the source.  The light behaves as if it has been emitted from a point source. Sometimes a beam, sometimes spreading as if from a point.   This is a diffraction phenomenon, but there is no obstacle causing the light to change direction. The change in direction is due to something other than an obstacle.
The behavior can be understood by noticing that the individual rays of light coming out of a laser have their origin from different atoms located at differnt parts of the laser cavity.  When the rays get outside of the laser, they all interfere in such a way that the propagation is like a beam nearby, but like a point far away. Do you see the word interfere there?
Let's return to the case of an obstacle in the path of the light. The light changes direction at the boundary.  You mentioned that yourself in the context of light spreading from the slits in Young's experiment. Why doesn't the light simply get blocked by the obstacle, so that on the other side of the slit you get "shadow" with a sharply defined edge.  You don't get that.  You get a semicircle.  The light intensity decreases at large angles, but it doesn't just shut off as if the obstacle were casting a shadow.  What's up with that?
The incident light excites individual atoms/molecules at the edge of the obstacle. Each individual atom/molecule then re-radiates.  But the atom/molecule is very small, a point source, so the light from each one of them spreads in a spherical pattern, every direction.  (This is how the light changes direction.) The light from each atom/molecule interferes with light from all the others (and with the rays that don't hit the obstacle), forming the intensity pattern that you see on the other side of the obstacle.  See the word interfere there?
Diffraction is an interference phenomenon.  And now we have a semantic mess and confused students.
Your intuition about a diffraction grating is correct, but it usually isn't described that way. We call it a diffraction grating, but perhaps it would be better called a diffraction-interference grating  That's an awkward word.
A: I would say your professor is wrong - or, at any rate, your account of their explanation is wrong.
A 'diffraction grating' is mis-named. It would be better to call it an interference grating.
'Interference' - as exhibited by Young's slits and by the the grating - involves adding amplitudes from a number of point sources (2 or N) and the phase differences give a pattern.
'Diffraction' - as exhibited by a single slit, a circular aperture, or an edge - involves integrating amplitudes over a single extended source, and the phase differences give a pattern.
So they are basically the same, but you get $\Sigma$ in the first and $\int$ in the second.
A real grating, or pair of slits, is not a point source but has a finite extent (or nothing would get through) and involves both.
this gives patterns like this (taken from https://en.wikipedia.org/wiki/File:Double-slit_diffraction_pattern.png)

where the green line comes from the convolution of the broad diffraction pattern, which depends on the width of the slits used, and the interference pattern which depends on the slit separation.
Adding more slits makes the green peaks narrower but does not change the fringe separation or the overall envelope.
