This paper investigates non-reduced-order event-triggered fixed-time synchronization (FxTS) and prescribed-time synchronization (PTS) for fuzzy inertial memristive neural networks with distributed delays (DFIMNNs). The original second-order model is directly analyzed to preserve the inertial structure and avoid dimension expansion. Memristive characteristics are introduced into both standard synaptic connection terms and fuzzy operation-related terms, and convex analysis is employed to handle state-dependent memristive switching, reducing the conservatism of the conventional maximum-absolute-value method. Based on this, an adjustable event-triggered controller (ETC) is designed, and sufficient criteria are derived to achieve FxTS and PTS while excluding Zeno behavior. Finally, numerical simulations and comparisons with a continuous controller verify the effectiveness of the proposed method and its advantages in reducing control updates.