Optical spectroscopy in high magnetic fields $B≤65$ T is used to reveal the very different nature of carriers in monolayer and bulk transition metal dichalcogenides. In monolayer WSe$_{2}$, the exciton emission shifts linearly with the magnetic field and exhibits a splitting which originates from the magnetic field induced valley splitting. The monolayer data can be described using a single particle picture with a Dirac-like Hamiltonian for massive Dirac fermions, with an additional term to phenomenologically include the valley splitting. In contrast, in bulk WSe$_{2}$ where the inversion symmetry is restored, transmission measurements show a distinctly excitonic behavior with absorption to the 1s and 2s states. Magnetic field induces a spin splitting together with a small diamagnetic shift and cyclotron like behavior at high fields, which is best described within the hydrogen model. ; Comment: just accepted in Nano Letters http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.5b00626 (equations corrected)