While significant progress has been made to fill the "THz gap", critical applications requiring powerful and energy efficient THz sources and amplifiers, from high frequency communications to medical and security imaging and nonlinear spectroscopy, continue to drive research on new methods of THz generation. Here we demonstrate a Free Electron Laser (FEL) THz source based on a novel interaction regime where broadband THz pulses can be phase and group velocity matched to the electron beam in a magnetic undulator via dispersion in a waveguide. Using < 10 pC, 6 MeV electron beams we show amplification of broadband THz pulses and demonstrate THz generation via both stimulated emission and spontaneous coherent superradiant emission, due to the short bunch length (< 200 fs rms) relative to resonant THz frequency (0.8 THz). A newly developed multifrequency simulation, designed to model the special case of guided FEL interaction, is benchmarked with the experiments and then used to extrapolate the capabilities of this "zero-slippage" FEL to efficient, tunable generation of > 100 μJ THz pulses when using higher (200 pC) beam charges and a tapered resonant condition.