Quasielastic excitation function measurement has been carried out for the ⁴He + ²³²Th system at θ_lab = 160° with respect to the beam direction, to obtain a representation of the fusion-barrier distribution. Using the present data along with previously measured barrier distribution results on ¹²C, ¹⁶O, and ¹⁹F+²³²Th systems, a systematic analysis has been carried out to investigate the role of target and/or projectile structures on fusion-barrier distribution. It is observed that for ⁴He, ¹²C, and ¹⁶O + ²³²Th reactions, the couplings due to target states only are required in coupled-channel fusion calculations to explain the experimental data, whereas for the ¹⁹F + ²³²Th system along with the coupling of target states, inelastic states of ¹⁹F are also required to explain the experimental results on fusion-barrier distribution. The width of the barrier distribution shows interesting transition behavior when plotted with respect to the target-projectile charge product for the above systems.