I'm looking for a short explanations describes the difference between the magnetic flux and magnetic flux density in the most easiest way.
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2 Answers
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To put it simply,
Magnetic flux is the amount of magnetic field passing through a given area. The unit is Tm2 or Wb.
Magnetic flux density is the amount of magnetic field passing through a unit area. The unit is Wb/m2 or T.
Think about it this way: normal density, as in the density of objects, is the mass per unit volume. To find the mass, you just multiply it by the volume. This is basically the same thing.
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In general, the density of a quantity $A$, let's call it $\varrho_A$, is the quantity that you need to integrate to get the quantity. For example, the density of the mass is the mass density, which you might be familiar from mechanics. The type of the integral depends on the situation. For example, you can have 1,2 and 3 dimensional mass densities and they require 1, 2, 3 dimensional volume integral respectively. In this case, the density is a scalar function, but in your case it's a vector, and the integral is not a volume integral but a surface integral, but the concept is the same: the flux of a surface $A$ id the integral of the density on that surface, i.e. $$\Phi_A=\int_A B \cdot \mathrm{d}S$$
