The prospects of utilizing single-carrier (SC) and multi-carrier (MC) waveforms in future terahertz (THz)-band communication systems remain unresolved. On the one hand, the limited multi-path components at high frequencies result in frequency-flat channels that favor low-complexity wideband SC systems. On the other hand, frequency-dependent molecular absorption and transceiver characteristics and the existence of multi-path components in indoor sub-THz systems can still result in frequency-selective channels, favoring off-the-shelf MC schemes such as orthogonal frequency-division multiplexing (OFDM). Variations of SC/MC designs result in different THz spectrum utilization, but spectral efficiency is not the primary concern with substantial available bandwidths; baseband complexity, power efficiency, and hardware impairment constraints are predominant. This paper presents a comprehensive study of SC/MC modulations for THz communications, utilizing an accurate wideband THz channel model and highlighting the various performance and complexity trade-offs of the candidate schemes. Simulations demonstrate that discrete-Fourier-transform spread orthogonal time-frequency space (DFT-s-OTFS) achieves a lower peak-to-average power ratio (PAPR) than OFDM and OTFS and enhances immunity to THz impairments and Doppler spreads, but at an increased complexity cost. Moreover, DFT-s-OFDM is a promising candidate that increases robustness to THz impairments and phase noise (PHN) at a low PAPR and overall complexity.