Background: Quasi dynamical symmetry (QDS) and partial dynamical symmetry (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: The goal of this paper is to establish a link between PDS and QDS and find an empirical manifestation. Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei. Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified. Conclusions: PDS is more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.