Polarization singularities beyond bound states in the continuums (BICs) have garnered significant interest due to their potential for light manipulation. The conservation of topological charge has proven crucial in various photonic systems, guiding the behavior of these singularities, including the generation and annihilation of BICs. This work theoretically reveals the simultaneous generation of two distinct polarization singularity types, which include off-Γ accidental BICs and Dirac-type band degeneracy points. The generation is driven by a quadratic degeneracy of symmetry-protected BICs in a photonic crystal slab. It should be noted that it is achieved through continuously tuning a geometric parameter without breaking symmetry. Importantly, the generation of both singularity types can be explained by the topological charge conservation law. This adherence ensures the stability of these singularities and allows for continuous tuning of their positions in momentum space by continuously tuning a geometric parameter while preserving symmetry. This study presents a novel framework for synthesizing and manipulating complex polarization states by combining polarization singularities from both BICs and band degeneracies, and holds promise for application in other wave systems beyond photonics.