ABSTRACT Some tidal disruption events (TDEs) exhibit blueshifted broad absorption lines (BALs) in their rest-frame ultraviolet (UV) spectra, while others display broad emission lines (BELs). Similar phenomenology is observed in quasars and accreting white dwarfs, where it can be interpreted as an orientation effect associated with line formation in an accretion disc wind. We propose and explore a similar unification scheme for TDEs. We present synthetic UV spectra for disc and wind-hosting TDEs, produced by a state-of-the-art Monte Carlo ionization and radiative transfer code. Our models cover a wide range of disc wind geometries and kinematics. Such winds naturally reproduce both BALs and BELs. In general, sightlines looking into the wind cone preferentially produce BALs, while other orientations preferentially produce BELs. We also study the effect of wind clumping and CNO-processed abundances on the observed spectra. Clumpy winds tend to produce stronger UV emission and absorption lines, because clumping increases both the emission measure and the abundances of the relevant ionic species, the latter by reducing the ionization state of the outflow. The main effect of adopting CNO-processed abundances is a weakening of C iv 1550 Å and an enhancement of N v 1240 Å in the spectra. We conclude that line formation in an accretion disc wind is a promising mechanism for explaining the diverse UV spectra of TDEs. If this is correct, the relative number of BAL and BEL TDEs can be used to estimate the covering factor of the outflow. The models in this work are publicly available online and upon request.