Why there are three equations governing blackbody emission? I learnt that the spectrum of a black body can be explained using


Planck distribution
Rayleigh -Jeans equation and
Weins displacement law


Can anyone tell me why there are three different equations that explain the same physical phenomena and when should I consider which equation?
Historically, two people (or groups of people) independently came up with different equations to model the blackbody equations in different parts of the spectrum. Rayleigh-Jeans law (classically derived) is valid for longer wavelengths and Wien's law (not Wien's displacement law) is valid for shorter wavelengths.

The Planck Distribution approaches the two laws in its limits, as in, for shorter wavelengths it is approximately equivalent to Wien's law and for longer wavelengths, it is approximately equivalent to Rayleigh-Jeans law. However, the quantum mechanically formulated Planck's law is accurate at all wavelengths, so it is the one that should always be used. One can use the other laws, for example, for brightness temperature definitions in radio astronomy, they use the RJ law for convenience, but that's because the wavelengths are long enough, and the approximation of the Planck's law gives the same result. (https://en.wikipedia.org/wiki/Planck%27s_law#Approximations)

Wien's displacement law only relates the peak wavelength to the temperature, which is a different law completely, though Planck's law (differentiating the function to find the maximum) also gives the same result. Though in this case, the displacement law is not approximate. It is accurate and can be used whenever you want.