We present a first-principles study of the GdRh2Si2(001) surface electronic structure. Two surfaces, Si- and Gd-terminated, are considered. The origin of the two-dimensional (2D) electronic states at both terminations is investigated by tracing the band structure evolution by going from individual Si, Rh, and Gd atomic layers to (non)stoichiometric ultrathin films and, finally, to thicker GdRh2Si2 slabs. We find the conic-like (Dirac-like) resonance state located in the vicinity of the Γ point at the Si termination to form via the Tamm mechanism and explain the reasons for the differences in dispersion and energy position of the resonance states at the Si and Gd terminations. Then, we show how the butterfly-like dispersion of the Shockley state, residing in the bulk projected band gap near the M point, appears due to the interaction of the bands localized in the surface and subsurface Gd-Si-Rh-Si blocks of the Si termination. Also, a giant sign-alternating atomic relaxation near both the Si- and Gd-terminated surfaces is revealed and its effect on the dispersion and energy position of the 2D states is discussed. In this way we shed light on the origin of the 2D states and explain their dispersion seen in angle-resolved photoemission spectroscopy experiments.