Nanosheets of transition metal dichalcogenides with prospects of photocatalysis and optoelectronics applications have significant potential in device fabrication due to their low-cost production and easily controllable morphology. Here, non-degenerate pump-probe differential transmission studies with varying pump-fluence have been carried out on single-phase 2H-MoSe2 and mixed-phase 1T/2H-MoSe2 nanosheets to characterize their excited carrier dynamics. For both the samples, the differential probe transmission data show photo-induced bleaching at earlier pump-probe delay followed by photo-induced absorption unveiling signatures of exciton-state filling, exciton trapping, defect-mediated photo-induced probe absorption and recombination of defect bound excitons. The exciton trapping and photo-induced absorption by the trapped-carriers are estimated to occur with time constant of ∼430 to 500fs based on multi-exponential modelling of the differential transmission till pump-probe delay of ∼3.5ps. Biexponential modeling of the subsequent slow-recovery of the negative differential transmission at pump-probe delay ≳3.5ps reveals that the exciton recombination happens via two distinct decay channels with ∼25 to 55ps (τ1) and ≳1ns (τ2) time constants. Pump-fluence dependent reduction in τ1 and further modelling of exciton population using higher order kinetic rate equation reveals that the two-body exciton-exciton annihilation governs the exciton recombination initially with a decay rate of ∼10-8 cm3s-1. The detailed analysis suggests that the fraction of total excitons that decay via long decay channel decreases with increasing exciton density for 2H-MoSe2, in contrast to 1T/2H-MoSe2 where the fraction of excitons decaying via long decay channel remains constant.