What is the difference between these mixing-angle equations?

In the following article the mixing angle of the neutrinos is given by:

$$sin^2 2theta = frac{mu^2}{mu^2 +[cGamma_alpha E /M +M/2]^2} tag{1}$$

where $mu$ represents the Dirac mass , M represents the Majorana mass for the right-handed components and $Gamma$ represents the collision rate .

But I was told that for neutrinos, based on a see-saw type I mechanism, and on the mass matrix the following is true :

$$mu^2 = sin^2 (theta) m^2_s tag{2}$$

What is the difference between these two? Is one of them in the vacuum and the other one not?