The fishtail magnetization observed in many type II superconductors has been investigated since the earliest nineties and associated with different phase transitions and dynamic crossovers in complex vortex matter. In systems without a sharp order-disorder phase transition, the fishtail has been related with a crossover from elastic to plastic vortex creep regimes. In this paper we perform a critical revision of this accepted picture. We show that, in slightly underdoped YBa₂Cu₃O_7-δ single crystals, there is a clear correlation between the fishtail magnetization and the Peak Effect observed in ac experiments with the associated history effects. We propose that both features are originated in the same dynamic crossover, between two plastic creep regimes. The proposed picture can also apply to other system, as those belonging to same families of iron-based pnictides.