To meet the required operation speed for protection of meshed voltage source converter (VSC) high voltage direct current (HVDC) grids, traveling wave-based algorithms operating in the sub-millisecond time-frame can be used. The domain in which these algorithms operate, i.e., modal or phase, determines their performance in fault discrimination, fault type classification and faulted pole selection. In the recent literature, high-speed algorithms have been proposed for various VSC HVDC grid configurations and transmission line types; yet the choice of domain has received insufficient attention. This paper offers recommendations for the choice of domain for protection algorithm design of HVDC overhead line or cable systems in symmetric monopolar and bipolar configurations. The theoretical analysis of this paper, which is based on fundamental wave propagation theory, indicates that the preferred domain for protection algorithms for cable and overhead line systems are the phase and modal, respectively. Furthermore, the paper provides comprehensive guidelines to construct detection functions for both configurations and discusses the errors introduced by approximations. Finally, study results from a bipolar overhead line test system demonstrate the advantages of modal over phase domain for fast fault discrimination and classification and illustrate practical problems associated with non-ideal detection functions.