What is a type of offensive operation that destroys or defeats enemy forces, seizes and secures terrain, or both?

The type of offensive operation that is specifically designed to destroy or defeat enemy forces, seize and secure terrain, or accomplish both objectives is an attack.

An attack can take various forms, including frontal assaults, flanking maneuvers, and ambushes, all of which aim to engage and defeat the enemy while simultaneously gaining control of important terrain. This operation is a fundamental aspect of military strategy, allowing forces to not only weaken the enemy through direct engagement but also to establish positions that may provide strategic advantages for subsequent operations.

In contrast, while the other terms describe various military actions, they do not encompass the comprehensive objectives of an attack. For example, a rout refers to a state in which enemy forces are dispersed or defeated, often as a result of a successful offensive operation, but it is not an operation in itself. Gain ground typically focuses on securing territory but lacks the explicit focus on defeating enemy forces. Overrun implies a rapid and often aggressive tactic where forces surge over the enemy, which can happen during an attack but does not capture the full strategic scope of seizing and securing terrain in conjunction with decisively engaging enemy units.