Short answers, pulled from the story.
Grand strategy is a state's plan for using all available means, military and nonmilitary, to advance national interests over the long term. It differs from foreign policy in that it weighs costs and benefits, sets priorities, considers military implications, and produces a practical plan rather than a list of ambitions and wishes.
British military historian B. H. Liddell Hart played an influential role in popularizing grand strategy in the mid-20th century. His definition, which emphasized coordinating all national resources toward a political objective and looking beyond war to subsequent peace, shaped most definitions that followed.
From the era of Hadrian, Roman emperors relied on preclusive security: a linear barrier of perimeter defenses with legions stationed in great fortresses along the frontier, including physical walls such as Hadrian's Wall. Rome's road network allowed troops and supplies to move quickly between frontiers, enabling the Empire to outlast invaders even when it could not defeat them in open battle.
Barry R. Posen and Andrew L. Ross identified four alternatives in a 1997 article: neo-isolationism, selective engagement, cooperative security, and primacy. Neo-isolationism called for withdrawal from NATO and reliance on nuclear deterrence; selective engagement called for intervention only in Europe, Asia, and the Middle East; cooperative security emphasized international institutions and collective action; primacy called for U.S. military preponderance and the prevention of peer competitors.
Restraint calls for reducing overseas security commitments while maintaining engagement with the international economy, including support for relatively open trade. Isolationism goes further by favoring restrictions on trade and immigration and holding that outside events have little impact on the United States. The two are distinct schools, though they are sometimes confused.
Offshore balancing holds that the United States should avoid significant overseas involvement except to prevent any single power from dominating Europe, Northeast Asia, or the Persian Gulf. It is associated with offensive realist theory and with political scientists Stephen Walt and John Mearsheimer, who have proposed it as an alternative to liberal hegemony.