The morphology of the Milky Way is still a matter of debate. In order to shed light on uncertainties surrounding the structure of the Galaxy, in this paper, we study the imprint of spiral arms on the distribution and properties of its molecular gas. To do so, we take full advantage of the SEDIGISM survey that observed a large area of the inner Galaxy in the $^{13}$CO(2-1) line at an angular resolution of 28". We analyse the influences of the spiral arms by considering the features of the molecular gas emission as a whole across the longitude-velocity map built from the full survey. Additionally, we examine the properties of the molecular clouds in the spiral arms compared to the properties of their counterparts in the inter-arm regions. Through flux and luminosity probability distribution functions, we find that the molecular gas emission associated with the spiral arms does not differ significantly from the emission between the arms. On average, spiral arms show masses per unit length of $\sim10^5-10^6$ M$_{\odot} $kpc$^{-1}$. This is similar to values inferred from data sets in which emission distributions were segmented into molecular clouds. By examining the cloud distribution across the Galactic plane, we infer that the molecular mass in the spiral arms is a factor of 1.5 higher than that of the inter-arm medium, similar to what is found for other spiral galaxies in the local Universe. We observe that only the distributions of cloud mass surface densities and aspect ratio in the spiral arms show significant differences compared to those of the inter-arm medium; other observed differences appear instead to be driven by a distance bias. By comparing our results with simulations and observations of nearby galaxies, we conclude that the measured quantities would classify the Milky Way as a flocculent spiral galaxy, rather than as a grand-design one.< Réduire