I tried to search the internet but could not find a direct comparison. Is there any link between supernova and helium flash? If so, what is it? otherwise how they are different?
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The helium flash is caused by the explosive ignition of helium in the electron-degenerate core of a low mass ($<2M_{\odot}$) star, that terminates the ascent up the red giant branch.
A supernova can be one of two basic types. A type II is the core collapse of a massive star ($>8M_{\odot}$). About the only point of similarity here is that the core of the star is supported by electron degeneracy pressure prior to the collapse. Not much else is similar, since there is no explosive fusion process inititated.
There is more similarity with a type Ia supernova. This is the explosive detonation of a white dwarf. The white dwarf has a similar mass to a degenerate He core, maybe a factor of two larger and is likely composed of carbon and oxygen, rather than helium, but is supported by electron degeneracy pressure. The supernova is initiated by the ignition (probably of carbon) at extremely high densities somewhere near the core of the white dwarf. Alternatively there are some models where the detonation is initiated by the ignition of helium closer to the surface.
In both a helium flash and a type Ia supernova, the basic physics principle is the same. Because the object is supported by electron degeneracy pressure, and because that degeneracy pressure is insensitive to temperature, then that gas is unstable to a runaway nuclear reaction. Most of the heat is used to raise the temperature of the ions in the gas, since degenerate electrons have a very small heat capacity.
In the case of a type Ia supernova, the process can completely destroy the white dwarf. In a degenerate helium core there is no destruction and in fact no visible sign even at the surface that the flash has taken place, I think this is because the density and level of degeneracy is much lower, so that once the temperature has risen a little the energy is used to expand the core and the overlying envelope. I suppose the total energy released during the helium flash is also much less than the binding energy of the star, whereas in a type Ia supernova the opposite is true, which is why the star is destroyed.
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$\begingroup$ Thank you Rob Jefferies. 1) So, we can say the two are not related in the sense, that when we see a supernova (1a), it is not a Helium flash. 2) Also, if Helium flash is not visible on the surface of the star, does that mean that we never observe it in the form of a flash? We may be observing it as expansion of star instead, How does it visually look like to outside world? $\endgroup$– kpvCommented Oct 16, 2016 at 16:55
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1$\begingroup$ @kpv (1) Supernovae are not He flashes. (2) The energy from the flash goes into removing the electron degeneracy and expanding the core. Nothing emerges (except perhaps neutrinos - there is another point of similarity, neutrino emission from the core) . The response of the star is to shrink. The flash comes at the end of the red giant phase and initiates the horizontal branch phase. $\endgroup$– ProfRobCommented Oct 16, 2016 at 16:58