a battle is simply a small event in a larger war

A battle is when two armies (if they both choose the place and time it's campal, if they don't is a skirmish, siege or ambush) clash with each other. Usually the most important aspect is the tactical one, while the strategic one my have impact for larger battles.

A war is an open conflict, made of many battles, where two states (or two informal sides if it's an informal war) compete militarily trying to beat their oponent. The logistical, intelligence and diplomatic aspects are more proper of this scale.

Hope it helps!

PD: If you want to know more things about this or history in general just ask, I gladly explain whatever you want to know!

A battle is a singular military action and a war is a series of military actions

A war is made up of a series of battles. Set and subset.

It is the same as being engaged and married

Very little on the political section of SW.

War is when the politicians fuck everything up, a battle is when the soldier are sent in to clean it all up.