Monte Carlo and theoretical studies of thin 3D films of biaxial and uniaxial nematics with tangential boundary conditions show distinct differences in structure and evolution of topological defects. In the uniaxial films, defects of strength k=+/-1 are point defects that bear no bulk singularity and disappear by annihilation with each other. In the biaxial films, k=+/-1 defects are true singular bulk disclinations that split into pairs of k=+/-1/2 lines; the latter disappear by annihilation processes of the type +1/2-1/2=0. These observed differences are of relevance for the current debate on the existence of biaxial phases.