Corner-supported modular steel buildings, made of volumetric bespoke prefabricated units, are one of the most efficient construction systems for the next generation of prefabricated prefinished building construction. In these systems, the influence of connections between the units, so-called inter-connections, on the distribution of forces, moments, stability, and deformations of the frame is the key to the overall structural performance that differentiates the design of these systems from that of their conventional counterparts. In the design of modular buildings, the structural properties of inter-connections, such as stiffness, strength, and rotation capacity, are elements directly impacting their performance. This paper proposes a classification system for rotational stiffness and strength properties of inter-connections in sway corner-supported modular frames. The stiffness' boundary values corresponding to the rigid/semi-rigid and semi-rigid/nominally-pinned zones are represented by parametric charts based on the variation of relative bending stiffness ratios of elements such as beams, columns, and joints. To develop the classification system corresponding to stiffness properties of inter-connections, three performance criteria are assumed as (i) buckling criterion, which represents the classification based on the ultimate limit state; (ii) displacement/drift criterion, which considers the behaviour of the structure in the serviceability limit state; and (iii) combined buckling and displacement/drift criterion at the ultimate limit state. Furthermore, inter-connections are classified into three categories of fully-strength, partial-strength, and nominally-pinned in terms of their strength properties based on the ultimate moment capacity of inter-connections. The proposed classification system can be employed in the initial phase of a modular structure design to classify joints, and select a proper design method and process according to their category. Numerical examples are included to verify the validity of the proposed classification system. Finally, design recommendations are suggested for the accurate design of inter-connections in sway corner-supported modular frames without the need for complicated nonlinear analyses.