Electrodynamic (ED) analysis of the TEn0p (TE theta phi r) modes in a shielded single-crystal-5-mm-diameter yttrium iron garnet (YIG) sphere has been performed and compared with the results of previous experiments. Measurements and ED analysis of the HE111 +/- mode resonances in a polycrystalline Al-doped rod-shaped YIG sample have been performed for comparison. It has been shown that electromagnetic resonances in large shielded YIG spheres behave in a similar way as typical resonances occurring in dielectric resonators under conditions when the effective permeability is positive, and as so-called magnon resonances when the effective permeability is negative. Nevertheless, both types of resonances are solutions to the same transcendental equation. Computations reported herein suggest that the physical nature of resonance systems containing dispersive gyrotropic media can be described within a common framework of electromagnetic resonance systems with unequal stored magnetic and electric energies, which offers an alternative to the more widely used quantum and harmonic oscillator models.