Perhaps we need to go back to the basics and define WAR and BATTLE and CAMPAIGN.
WAR
1. a conflict carried on by force of arms, as between nations or between parties within a nation; warfare, as by land, sea, or air.
2. a state or period of armed hostility or active military operations: The two nations were at war with each other.
3. a contest carried on by force of arms, as in a series of battles or campaigns: the War of 1812.
The two nations were Carthage and Rome.
Those nations primarily were based in different continents with a sea between them. One nation launches a war on the other and the nations have a sea between them. I do not count Spain as an integral part of Carthage, it was a colony and on net took more resources from Cartage then it provided Hannibal.
Battle
1.a hostile encounter or engagement between opposing military forces: the battle of Waterloo.
2.participation in such hostile encounters or engagements: wounds received in battle.
3.a fight between two persons or animals: ordering a trial by battle to settle the dispute.
Campaign
1.Military .
a. military operations for a specific objective.
b. Obsolete . the military operations of an army in the field for one season.
2. a systematic course of aggressive activities for some specific purpose: a sales campaign.
3. the competition by rival political candidates and organizations for public office.
The overseas war that Carthage launched on Rome started with a campaign launched from a base/colony in Spain where many recruits were gained and many battles occurred.
See, IL, the problem is you don’t know meaning of basic words. But again, you were sure Hannibal was born in Turkey so its no wonder big words confuse you. Please consult a dictionary before engaging in a battle wits with me as you are poorly armed.