Sure. When the military murdered and/or raped 300+ villagers in My Lai, it was a very serious offense. The commander (lieutenant) was ultimately charged 22 counts of murder, and served a very hard three years of house arrest.
As you can see, the charges are quite serious, which can exceed 3 days stuck in house per instance of illegal homicide.
The way this is usually handled with smaller crimes (DUI) is that the local civilian court gets “dibs” but the military installation can ask to discipline someone under the military system (Uniform Code of Military Justice, UCMJ). Usually the locals are happy to let a military person be disciplined by the military. It keeps the burden off the civilian system, which usually has plenty of other cases to get through. Plus, the military can do things that the civilian court can’t, like reducing a person’s rank.
If the civilian court wants to make an example out of the military member they can opt to keep the case in their court. This can happen if the crime was egregious or there are some other circumstances. Plus, any additional civil suit brought by a victim or their family will always be a civilian lawsuit.
There are times where things are different- in particular, there are times in which something is only a crime in one system but not the other. You can be court-martialled for failing to follow orders, but this is not a civilian crime.
In terms of shooting a civilian, it probably depends on the circumstances. If the Marine was given an order to shoot and had some legitimate feeling reason to do so in the moment, the military would probably do their best to protect the marine, but it would probably be a civilian court trying them (the military won’t take a case if they don’t intend to follow through). Note that for this to be the case, there is probably now an officer who gave an illegal order and the officer would probably be tried for a crime. But there are conceivable ways in which a marine can shoot someone under lawful orders and not really have done anything wrong- self defense is the likely scenario. If a protestor starts shooting a gun toward a marine then they will get return fire.
If the marine were to disregard his orders and shoot someone because he’s trigger happy, then the military is probably going to ask to take the case, throw him in prison for life while demoting him down to E1 (the lowest rank), and generally ruin his life as much as they can. They really crack down on this kind of thing because they rely on discipline to make things work. Marines are generally trained to do as they are told, no matter how much it sucks. And marines that don’t do as they’re told get examples made out of them so that everyone else knows to follow orders.
At least that’s what would have happened in the past, but with the current president who knows how it would turn out. Because the state may choose not to let the case go- the president can pardon a federal/military crime, but not state crimes. So California might keep the case because then the president couldn’t let him off easy.
Outside of military installations, a member of the US military may be subject to prosecution for any crimes committed under both civilian criminal law and the UCMJ. DUI is the most common scenario for this.
In this case, I would imagine it'd be none, because Trump as commander-in-chief would give orders to military courts to not prosecute, and grant pardons to anyone who gets dragged into the civilian court.
They'll be prosecuted by Kevin Bacon, with Tom Cruise as their defense attorney, and with Jack Nicholson giving a rousing testimony in which he confesses that he is the one who gave the order to the marines to commit the crime.
