We analyse the physical properties of 121 SNR $geq$ 5 sub-millimetre galaxies (SMGs) from the STUDIES 450-$mu$m survey. We model their UV-to-radio spectral energy distributions using MAGPHYS+photo-$z$ and compare the results to similar modelling of 850-$mu$m-selected SMG sample from AS2UDS, to understand the fundamental physical differences between the two populations at the observed depths. The redshift distribution of the 450-$mu$m sample has a median of $z$ = 1.85 $pm$ 0.12 and can be described by strong evolution of the far-infrared luminosity function. The fainter 450-$mu$m sample has $sim$14 times higher space density than the brighter 850-$mu$m sample at $z$ $lesssim$2, and a comparable space density at $z$ = 2-3, before rapidly declining, suggesting LIRGs are the main obscured population at $z$ $sim$ 1-2, while ULIRGs dominate at higher redshifts. We construct rest-frame $sim$ 180-$mu$m-selected and dust-mass-matched samples at $z$ = 1-2 and $z$ = 3-4 from the 450-$mu$m and 850-$mu$m samples, respectively, to probe the evolution of a uniform sample of galaxies spanning the cosmic noon era. Using far-infrared luminosity, dust masses and an optically-thick dust model, we suggest that higher-redshift sources have higher dust densities due to inferred dust continuum sizes which are roughly half of those for the lower-redshift population at a given dust mass, leading to higher dust attenuation. We track the evolution in the cosmic dust mass density and suggest that the dust content of galaxies is governed by a combination of both the variation of gas content and dust destruction timescale.
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