Contest, conflict, combat, fight, affray, fray denote a battle between opposing forces for supremacy, for power, or for possessions.
Contest is the broadest term; originally it referred solely to strife in argument but it is now applicable to any struggle, whether friendly or hostile, for a common object that involves a test of ability, strength, endurance, or strategic skill.
Conflict implies discord and warfare; it also suggests a closer engagement than contest. Conflict may be extended to denote a struggle (often spiritual or mental) between opposing or contradictory principles or forces.
Combat is less commonly used in an extended sense. It implies an encounter, especially an armed encounter, between two (individuals, parties, or forces), frequently for the determination of a dispute.
Fight usually implies a hand-to-hand conflict and therefore emphasizes the individual participants. It ranges in dignity from a spiritual struggle to actual blows with fists or weapons.
Affray commonly refers to a tumultuous disturbance (as a street fight between mobs or factions) that inspires terror.
Legally an affray is a fight that disturbs the public peace; in literary use the word is often applied to an unseemly or acrimonious dispute.
Fray is usually either a literary term, often with more dignified connotations than affray of which it is otherwise a very close synonym, or it is a poetic or hyperbolical substitute for battle, contest, or game.