Everyone knows the difference on some level. We have all seen two people scuffle over something simple. Sometimes there are shoves, slaps, even punches, kicks and tackling. There is certainly a lot of noise.
That situation is a fight.
At the end of it people may be bruised, broken, and a little bloody but they will heal and may even share a beer and a laugh afterwards.
Combat is when one or both people are in danger of getting seriously injured or killed. Combat can start right at the beginning of an altercation or be the result of someone upping the ante during a fight. A clear sign of combat is that people watching are terrified. Bystanders usually try and break up fights at the point they are about to escalate, otherwise they just let the fight wind down on its own. When combat breaks into the equation it is downright stupid to try and get in the middle, everyone is in danger at that point.
Most plays deal with combat. The stakes are set to be life or death. The movements for life and death combat are different than for a fight. The intensity is through the roof, the strikes are meant to maim or kill, the movements are quick and energized.
In a fight, the strikes are meant to hurt but not kill. There may be moves that knock the other person out or pound on them a bit but the intention is to dominate/win or teach a lesson, etc.
It is important to differentiate what situation you have in the play. Knowing whether its a fight or combat will help establish the intentions, intensity, movements, vocals, and story.