Three ternary thiophosphates α-BaPS, β-BaPS, and PbPS were synthesized via a high temperature salt flux method or an I2 transport reaction. β-BaPS and PbPS were previously structurally characterized without investigating their optical properties. α-BaPS was discovered for the first time, and it is isostructural to PbPS and crystallizes in the acentric space group Pn (no. 7). β-BaPS crystallizes in the centrosymmetric space group P21/n (no. 14). There is a high structural similarity between α-BaPS, β-BaPS, and PbPS including close unit cell parameters and identical [P2S6] motifs. The structural relationships between α-BaPS and β-BaPS, and β-BaPS and PbPS were elucidated by single crystal X-ray diffraction, differential scanning calorimetry (DSC), electronic structure calculations, and nonlinear optical property measurements. There are no phase transitions detected between α-BaPS and β-BaPS. From centrosymmetric β-BaPS to acentric PbPS, the chemical characteristics of Pb, such as stereoactive lone pairs, play a key role in the structural difference. PbPS is uncovered as a type-I phase-matching material with a moderate second harmonic generation (SHG) response of 1.4 × AgGaS and a high laser damage threshold (LDT) of 2.5 × AgGaS. α-BaPS is not a type-I phase-matching material with a moderate second harmonic generation response (1.7 × AgGaS, a sample of 225 μm particle size) and a high laser damage threshold (5.5 × AgGaS).