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Using a new full-vectorial finite-difference mode solver utilizing a hexagonal Yee's cell, we calculated the dispersion diagram of a slightly multimode (16 modes) air-core photonic-bandgap fiber (PBF) and the electric-field profiles of all of its core modes. Careful comparison shows striking similarities between these properties and those of the hybrid modes of a conventional step-index fiber, in terms of the modes' field profiles, the modes' degeneracy, the order in which the modes mode cut off in the wavelength space, and the maximum number of modes. Based on these similarities, we propose for the first time a systematic nomenclature for the modes of a PBF, namely hybrid HE and EH modes and of quasi-TE and quasi-TM modes. Other small but relevant similarities and differences between the modes of these two types of fibers are also discussed.