The advent of the JWST has revolutionised our understanding of high-redshift galaxies. In particular, the NIRCam instrument on-board JWST has revealed a population of Hubble Space Telescope (HST)-dark galaxies that had previously evaded optical detection, potentially due to significant dust obscuration, quiescence, or simply extreme redshift. Here, we present the first NIRSpec spectra of 23 HST-dark galaxies (\(\mathrm{H-F444W>1.75}\)), unveiling their nature and physical properties. This sample includes both dusty and quiescent galaxies with spectroscopic data from NIRSpec/PRISM, providing accurate spectroscopic redshifts with \(\mathrm{\overline{z}_{spec} = 4.1 \pm 0.7}\). The spectral features demonstrate that, while the majority of HST-dark galaxies are dusty, a substantial fraction, \(\mathrm{13^{+9}_{-6} \%}\), are quiescent. For the dusty galaxies, we have quantified the dust attenuation using the Balmer decrement (\(\mathrm{H\alpha / H\beta}\)), finding attenuations \(\mathrm{A_{V} > 2\ mag}\). We find that HST-dark dusty galaxies are \(\mathrm{H\alpha}\) emitters with equivalent widths spanning the range \(\mathrm{ 68 A < EW_{H\alpha} < 550 A }\), indicative of a wide range of recent star-formation activity. Whether dusty or quiescent, we find that HST-dark galaxies are predominantly massive, with 85\% of the galaxies in the sample having masses \(\mathrm{log(M_{*}/M_{\odot}) > 9.8}\). This pilot NIRSpec program reveals the diverse nature of HST-dark galaxies and highlights the effectiveness of NIRSpec/PRISM spectroscopic follow-up in distinguishing between dusty and quiescent galaxies and properly quantifying their physical properties. Upcoming research utilising higher-resolution NIRSpec data and combining JWST with ALMA observations will enhance our understanding of these enigmatic and challenging sources.