Off the top of my head, I'm thinking revenge is an act performed by one who perceives they have received an insult or injury perpetrated by another. The level and extent of the actions taken to affect a revenge against a perpetrator are at the sole discretion of the aggrieved party. Generally, I think an expectation of "an eye for an eye" level of response is considered a baseline level of response, although there really is no limit other than that set by the mores of the one seeking revenge and as such, the response has the potential to greatly exceed the instigating harm.
Justice, in my view, is a societal standard for punishment of a transgressor or assignment of required redress due the injured party. I see justice as governed by legal statute and social mores and norms. I would also say that it is societal institutions that would decide whether an injury or insult occurred as opposed to it being at the sole discretion of a claimant. My interpretation would be that justice would seek equivalency, in level or extent, between the harm done and the consequential punishment or redress that would be assigned in response. This would contrast with the potential excessive response that may occur with revenge.
In the ideal world, this is a good rational approach and a good contrast. But in the real world, where cultural and social justice falls short or is corrupt, revenge is often the last option for justice to be served.
For example, assaulting a police officer is considered a crime in the USA, unless you are an illegal alien within the Democrat run NYC injustice system. The just result, for that officer, did not occur. There is lingering justice deficit. Revenge at the discretion of the police officer, who was abused, is what is left, if the goal is justice and the justice system is perverted. The harmed police officer should be allowed a very moderate beat down of the perp, since the offenders were not super abusive. Then they can both go their own ways, satisfied and atoned.
Revenge is most common when the institutional justice system, is unjust, and/or when people feel injustice remains. Sometimes, the accused may get off on a technicality. The victim's family and everyone knows justice was not served. However, the civil authorities may have no mechanism, to serve justice. The family, to find closure, takes justice into their own hands.
Injustice can then multiply, due to the first lingering injustice, caused by the technicality. It leads to a second legal injustice; family man ends in jail for metering justice, while the original perp is free to do it again. Revenge happens when social justice breaks down. Revenge is more common in corrupt places. The prospect of revenge for severe social injustice, leads to social purges, so this at the top can avoid justice; Stalin.
For example, in the Middle East, revenge is being sworn by the Palestinians. Israel is the top dog and the bottom dog, Palestinians, do not feel they have had their justice, either subjectivity or objectivity. Cries of revenge and desperate actions is what it left when social justice fails to provide justice. Israel is now less about cries of revenge, since they have had a good spell of military revenge. This revenge cycle is all due to international law, not being able to satisfied either party, for all the mutual injustices. It is left for those who feel the worse.
If we go back to the police assault by the illegal immigrants; Elon Musk said, the Democrat party sees all illegal immigrants, as potential future votes for the DNC. They do not wish to put any in jail, since that could mean loss votes. Felons cannot vote. Injustice lingers.
Say Musk is right, and illegal immigrant crime, will be ignored to curry favor and not lose votes. Where does citizen victim justice come from, in such a case, if the social means for justice is corrupted for votes and power? It may need a tough hand, for political revenge, to right the wrongs of the criminals who have set up the injustice system; Banana Republic.
An interesting case is the slavery reparation scam, created by the DNC, to fake-buy black votes. This was used before and again it is money promise but not promises kept. The DNC had created a feeling of injustice about slavery, to people who were not slaves. Their revenge is to be extracted with money, to punish those, who did not have slaves; all tax payers.
This injustice felt by those who were not slaves, will create a secondary level of injustice to real time victims who are harmed today. They may now feel the need for revenge of the tangible crimes. The goal is actually racial division, via the dual revenge, using fake money promises to buy black votes who will take the side of money; DNC promises.
I hope the blacks do not fall for this scam. It comes from the Democrat Party, which was the party of slavery, that tries to form a separate county where slavery could life on forever. The slavery party of 1860's still has the same name; Democrat Party. it had in 1850's. Rather than waste your time on the DNC scam revenge; for votes, the DNC, itself , is the tangible place; law suit, to get your money.
The DNC has the same name then as 1825. DNC and their donors are deep pockets with a direct name connection; direct legal descendants of the main liability.
In my own experience with contractors, if they rip someone off, and retain the same name you can sue. But if they changes their name and form a new LLC, the old company is dissolved and old debts are hard to get back. The DNC never changed the name, even after they decided to divide the country to have a slave country in 1860's. If the DNC had won the war, many generation may still have been slaves. If the blacks want reparations, the DNC has a continuous legal name and incorporation connection liability, that can hold up in court for damages. You need to do it before they change their name. Get a finger in the pie, early and you will be covered.