The synthesis of the new equiatomic RScSb (R = La-Nd, Sm, Gd-Tm, Lu, Y) compounds has been recently reported. These rare earth compounds crystallize in two different crystal structures, adopting the CeScSi-type (I4/mmm) for the lighter R (La-Nd, Sm) and the CeFeSi-type (P4/nmm) structure for the heavier R (R = Gd-Tm, Lu, Y). Here we report the results of neutron diffraction, magnetization and heat capacity measurements on some of these compounds (R = Ce, Pr, Nd, Gd and Tb). Band structure calculations have also been performed on CeScSb and GdScGe (CeScSi-type), and on GdScSb and TbScSb (CeFeSi-type) to compare and understand the exchange interactions in CeScSi and CeFeSi structure types. The neutron diffraction investigation shows that all five compounds order magnetically, with the highest transition temperature of 66 K in TbScSb and the lowest of about 9 K in CeScSb. The magnetic ground state is simple ferromagnetic (τ = [0 0 0]) in CeScSb, as well in NdScSb for 32 > T > 22 K. Below 22 K a second magnetic transition, with propagation vector τ = [¼ ¼ 0], appears in NdScSb. PrScSb has a magnetic structure within, determined by mostly ferromagnetic interactions and antiferromagnetic alignment of the Pr-sites connected through the I-centering (τ = [1 0 0]). A cycloidal spiral structure with a temperature dependent propagation vector τ = [δ δ ½] is found in TbScSb. The results of magnetization and heat capacity lend support to the main conclusions derived from neutron diffraction. As inferred from a sharp peak in magnetization, GdScSb orders antiferromagnetically at 56 K. First principles calculations show lateral shift of spin split bands towards lower energy from the Fermi level as the CeScSi-type structure changes to the CeFeSi-type structure. This rigid shift may force the system to transform from exchange split ferromagnetic state to the antiferromagnetic state in RScSb compounds (as seen for example in GdScSb and TbScSb) and is proposed to explain the change-over from a ferromagnetic structure as found in the CeScSi-type compounds CeScSb and NdScSb to the antiferromagnetic state as found in TbScSb and GdScSb.