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We report experimental and theoretical investigations of emergent properties of heterostructures with one- or two-unit cells of SrRuO₃ (SRO) between two materials, SrTiO₃ (STO, insulating, diamagnetic) or CaRuO₃ (CRO, metallic, paramagnetic). In STO⁵/SRO¹/STO⁵, where the RuO₆ octahedra network is not continuous across the interface, SRO is cubic and the film is nonmagnetic and insulating, but in CRO⁵/SRO¹/CRO⁵, the RuO₆ octahedra network is continuous, the structure is orthorhombic and the film is ferromagnetic (FM) and metallic. Transmission electron microscopy/spectroscopy show no octahedral tilts in STO⁵/SRO¹/STO⁵ while in the CRO⁵/SRO¹/CRO⁵ the tilt angle is larger than in bulk SRO. STO⁵/SRO²/STO⁵ is strongly FM [T_C~120K] replicating a Curie-Weiss behavior. CRO⁵/SRO²/CRO⁵ is FM with slightly larger , exhibiting magnetism similar to a Griffiths phase. Density-functional-theory (DFT) calculations reproduce and provide insights into the structural, electronic and magnetic properties of the heterostructures. The highly localized Ru 4d orbitals are responsible for both the insulating and nonmagnetic behavior in STO⁵/SRO¹/STO⁵. Our study shows that in the ultrathin limit, a continuous RuO₆ octahedra network is key to the magnetic behavior of ruthenates.