Fight
: to use weapons or physical force to try to hurt someone, to defeat an enemy, etc. : to struggle in battle or physical combat
: to be involved in (a battle, struggle, etc.) involving the exchange of physical blows or the use of weapons.
Fighting
would be performing the above.
Conflict
: a struggle for power, property, etc.
: strong disagreement between people, groups, etc., that results in angry argument
: a difference that prevents agreement : disagreement between ideas, feelings, etc.
These definitions are from Webster’s Dictionary
All fighting is conflict but conflict isn’t necessarily fighting.