In the present work, type I, II, and III heterostructures are constructed with the same base material using three representative functionalized monolayer scandium carbides (Sc2CF2, Sc2C(OH)2, and Sc2CO2) by first-principles calculations based on density functional theory. In contrast to general bilayer heterosystems composed of two-dimensional semiconductors, type I and III heterojunctions are obtained in one Sc2CF2/Sc2CO2 system and the remains of the functionalized Sc2C heterostructures, respectively. It is noteworthy that the same monolayer Sc2CF2 and Sc2CO2 constituents lead to dissimilar heterostructure types in the two Sc2CF2/Sc2CO2 systems by modifying the stacking interface. In addition, in the two Sc2CF2/Sc2CO2 systems, remarkable changes in the heterojunction type are induced by a strain, and two distinct type-II heterostructures are generated where one layer with the conduction band minimum state and the other layer including the valence band maximum level are different. The present work suggests an attractive direction to obtain all heterostructure types with the same base material for novel nanodevices in various fields such as photonics, electronics, and optoelectronics using only the two monolayer components Sc2CF2 and Sc2CO2.