Hello,
When using TB2J with VASP-Wannier90, the magnetic moment is from the Wannier functions. It computes the density matrix from the Wannier function Hamiltonian and then computes the magnetic moments, so no reading of the magmom from VASP output is done.
The unit is the same (Bohr magneton). Indeed the magnetic moments should be close to the DFT result. But it doesn't have to be exactly the same. In VASP, the magmom is integrated inside the paw sphere by default. And in TB2J, it uses the projection to the Wannier functions.
If the numbers are too different, indeed it hints there are problems (often in the Wannierization procedure).
Best,
HeXu