The phase diagrams and phase transitions of a typical bilayer fractional quantum Hall (QH) system with filling factor ν = 2/3 at the layer balanced point are investigated theoretically by finite size exact-diagonalization calculations and an exactly solvable model. We find some basic features essentially different from the bilayer integer QH systems at ν = 2, reflecting the special characteristics of the fractional QH systems. The degeneracy of the ground states occurs depending on the difference between intralayer and interlayer Coulomb energies, when interlayer tunneling energy (Δ_SAS) gets close to zero. The continuous transitions of the finite size systems between the spin-polarized and spin-unpolarized phases are determined by the competition between the Zeeman energy (Δ_Z) and the electron Coulomb energy, and are almost not affected by Δ_SAS.