An optical wireless communications system which employs either intensity-modulation and direct-detection (IM-DD) or heterodyne detection (HD) is considered. IM-DD has lower complexity and cost than HD, but on the other hand, has lower capacity. It is therefore interesting to investigate the capacity gap between the two systems. The main focus of this paper is to investigate this gap at high SNR. Bounds on this gap are established for two cases: between IM-DD and HD, and between IM-DD and an HD-PAM which is an HD system employing pulse-amplitude modulation (PAM). While the gap between IM-DD and HD increases as the signal-to-noise ratio (SNR) increases, the gap between IM-DD and an HD-PAM is upper bounded by a constant at high SNR.