Is wave superposition always equivalent to wave interference? I'm confused when using these 2 words "wave superposition" and "wave interference" since their definition is very similar. 
So, are these 2 term the same?
 A: We say "superposition" when we talk about the adding of the amplitudes of two waves. Typically it is called "interference" when this adding results in an different waveform (for example, regions with no signal - like the fringes in Young's slits experiment). However really all interference is superposition, and all superposition is a form of interference.
A: Interference is an effect of superposition. If you add two waves of close amplitudes, the interference picture will be the strongest. If one of the waves is of a much smaller amplitude, the resulting wave will be that of the highest amplitude, practically with no interference effect.
A: Diffraction is the result of the influence of an edge on a wave. Behind every edge an electromagnetic radiation forms a fringe pattern. This is an intensity distribution and is called the interference pattern. Behind two close together lying edges (a slit) both EM radiation and water waves form intensity distributions. The only difference is that the interference pattern for EM radiation is stationary and it is non-stationary for water waves. 
A superposition is the summation of two interfering waves. In the special case of two planar water waves of the same frequency and amplitude both waves vanish completely, whose energy is converted into heat.
