Sodium-ion batteries (NIBs) have recently received great attention as a potential complement to existing lithium-ion battery (LIB) technology. Due to the difference between Na and Li in nature, what has been an attractive anode material for LIBs may or may not be utilized for NIBs.Using density functional theory calculations, we examine and compare the sodiation behaviors of Si, Ge, and Sn, in comparison also to their lithiation processes if needed. We evaluate single Na incorporation in the host matrices (M = Si, Ge, Sn) and also discuss the formation of Na-M alloys in terms of structural evolution and energetics, along with their mechanical and diffusion properties. While the alloy systems considered in this work appear to undergo similar transformation during sodiation and lithiation, the M networks tend to lose connectivity more rapidly in the former. At Na/Li:M = 1:1 ratio, the M networks in a-NaM alloys already disintegrate into compact isolated clusters while those in a-LiM still maintain extended connectivity via puckered conformation. This unique difference in their specific atomic arrangements contributes to the more rapid softening, larger volume expansion, and faster increase in Na diffusivity with sodiation in comparison to the case of lithiation.