We report two distinct superconducting states with different crystal structures and a crossover from a type-II to a type-I superconductor (SC) in (Ba, Sr)Bi-3. The superconducting parameters are revealed to classify two SCs: BaBi3 is in the weak-coupling limit on the basis of Delta C/gamma T-n(c )similar to 0.67 and 2 Delta/k(B)T(c) similar to 3.28 while SrBi3 is a strong-coupling SC with Delta C/gamma T-n(c )similar to 2.41 and 2 Delta/k(B)T(C) similar to 6.09. A large Kadowaki-Woods ratio (R-KW similar to 3.53a(0)) suggests an enhanced electron-electron scattering in BaBi3. With increasing the pressure, the T-c of BaBi3 decreases linearly at first, and then shows an abrupt increase up to 6.2 K at 0.88 GPa. This behavior can be attributed to a pressured-induced structural transition and the resulting variations of spin-orbit coupling and Fermi structures. T-c of SrBi3 is suppressed monotonously by pressure. The Ginzburg-Landau parameter kappa(GL) of BaBi3 decreases from 10.35 at ambient pressure (AP) to 0.86 at 1.75 GPa, and then tends to saturation. kappa(GL) of SrBi3 decreases from 0.76 at AP to 1/root 2 at 1.20 GPa, which manifests pressured-induced crossover from a type-II to a type-I SC. Possible physical mechanisms are proposed.