Three ternary thiophosphates α-Ba2P2S6, β-Ba2P2S6, and Pb2P2S6 were synthesized via a high temperature salt flux method or an I2 transport reaction. β-Ba2P2S6 and Pb2P2S6 were previously structurally characterized without investigating their optical properties. α-Ba2P2S6 was discovered for the first time, and it is isostructural to Pb2P2S6 and crystallizes in the acentric space group Pn (no. 7). β-Ba2P2S6 crystallizes in the centrosymmetric space group P21/n (no. 14). There is a high structural similarity between α-Ba2P2S6, β-Ba2P2S6, and Pb2P2S6 including close unit cell parameters and identical [P2S6] motifs. The structural relationships between α-Ba2P2S6 and β-Ba2P2S6, and β-Ba2P2S6 and Pb2P2S6 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-Ba2P2S6 and β-Ba2P2S6. From centrosymmetric β-Ba2P2S6 to acentric Pb2P2S6, the chemical characteristics of Pb, such as stereoactive lone pairs, play a key role in the structural difference. Pb2P2S6 is uncovered as a type-I phase-matching material with a moderate second harmonic generation (SHG) response of 1.4 × AgGaS2 and a high laser damage threshold (LDT) of 2.5 × AgGaS2. α-Ba2P2S6 is not a type-I phase-matching material with a moderate second harmonic generation response (1.7 × AgGaS2, a sample of 225 μm particle size) and a high laser damage threshold (5.5 × AgGaS2).