When I look at what happened in Cambodia, I notice it is different than the Holocaust or the Rwandan genocide in that in those cases it was one group killing another group, where in Cambodia it was one group killing themselves. Is this a fair assumption or am I missing something.
This is a large and complex question - and there is a healthy amount of debate within the relevant scholarship in regards to the use of the term 'genocide' in the context of Democratic Kampuchea and the policies of the CPK (Communist Party of Kampuchea)
First of all, yes it is qualitatively different to what happened during the Holocaust and the Rwandan genocide. Let me elaborate on that point before getting to the main part of your question.
You allude to the revolutionary period in Cambodia being characterised by Khmer killing Khmer. And this is accurate, but not the entire picture. Lets start by breaking down the different kinds of killing the KR are responsible for and when these distinct periods took place. After that we will discuss the use of the term genocide, and how the term doesn't really map onto the revolutionary period in Cambodia as a whole.
The Democratic Kampuchea regime was born out of the civil war which engulfed Cambodia from the late 1960s to the wars end when the Khmer Rouge seized power in April 1975. The first acts of violence perpetrated by the new regime were aimed at the previous government - the so called 'Lon Nol Regime'. Being associated with a high level or status of this regime was often met with execution. Sirik Matak, Lon Non (Lon Nol's brother) and others were executed almost immediately after the fall of Phnom Penh. Following this, members of the armed forces were instructed to surrender themselves and were too often executed en masse. Checkpoints that were placed outside of the major cities checked peoples occupations and apart from a very select few (some useful groups such as engineers were actually used by the KR to continue industrial work/automotive repairs etc) being a prominent member of the old regime was usually met with killing. Lets call that the first wave of executions. Many people died in the evacuation of the major cities but I will save that point for later.
The second massive amounts of executions took place after 1976 when internal purges began, this means that the Party looked inward to 'reactionary elements' within their own ranks and had these cadre sent to security centres (like S-21) where they were tortured, their 'confessions' extracted, and then they were executed. A common misconception is that the photos one sees at S-21 were just civilians sent to this prison. That is not the case, they were mostly cadre or soldiers or the families of these men. This is not 100% the case, many were unwitting civilians but the majority were cadre.
The purges of the East Zone increased in their reach because of the 'paranoia' of a Vietnamese plot to topple the CPK government. This was not completely unfounded. But this leads us to phrases like 'Khmer bodies with Vietnamese minds' being thrown around by the regime and cadre in order to identify the 'other' that they were targetting - the Vietnamese. Tens of thousands were executed in these purges.
So that is two different aspects of the KR executions. the first was against former government officials and peoples. The other against the regime's own ranks.
The third group of people who fall into an 'enemy' category for the KR was people who did not 'cultivate a proletarian consciousness'. This slogan gives us an insight into KR ideology and how it effected their motivations to 'smash' enemies. So the CPK ideologues faced a problem when trying to implement Marxist-Leninist doctrine in Cambodia; Cambodia barely had a 'working class'. Without getting too deep on the implications of these economic ideas - lets just reduce it to Orwellian conceptions like "Wrongthink". Basically the regime needed to cultivate a kind of 'state of mind' in the population in order to pursue its goals of purification of the land and its people. If you committed thought crimes, or were seen to not be 'sharpening your revolutionary consciousness' then you could be targeted by the regime. For example, someone stealing some extra fruit from the communal plantation would be seen as having 'the wrong consciousness' and therefore have shown a lack of revolutionary zeal. Being sick was often seen as the result of having the wrong consciousness. You were a 'regressive element', and the cadre who were in control of these communes had fairly vague orders to get rid of these kinds of people. Execution was the easiest method.
These kinds of killings, which is what I believe most people associate the Khmer Rouge with (and not for the wrong reasons) does not make up the majority of how people died in Cambodia. Most 'ordinary' people who died during the regime's time in power died from malnutrition and disease. The numbers here are up for debate however and I have seen estimates as high as one million from execution.
Now lets talk about 'genocide'. None of the examples I have given, these three kinds of killings, fall into the UN definition of genocide. Which is a legal term designed to have a fairly limited scope of use. The categories that are missing or too diffuse are: Intent. There was no explicit intent on behalf of the KR to kill all the Cambodians. Target Groups: Many scholars stretch the killings of enemies of the regime (the purges, killing old government people and ordinary people who were 'regressive') to be a political distinction (in that these people were killed for political reasons) the UN genocide definition does not count political groups as qualifiers.
Here is where we can use the term however, an ethnic muslim minority known as the Cham probably lost about one third of their entire population during the regime, likewise the Vietnamese left in KR after 1975 were basically all killed. So in the case of the Cham we have a death rate higher than the average citizen. Why is this the case?
Well there are two schools of thought on the matter. If you follow Ben Kiernan's line it would be because the Cham were targeted by the CPK because of 'who they were', that is that they were persecuted on racial grounds. They were forced to eat pork, they were not allowed to practise their religion. They were broken up around the nation and classed as 'depositees' (new people) despite their status being more akin to the 'old people'. So without getting very deep on this one - There are ground to consider the treatment of the Cham as genocidal. There is seeming intent to wipe them all out - and this was done because of their race. (Like I said that is one side of the argument - Steve Heder claims that it was a class distinction and therefore it falls out of the UN classification)
The other group I mentioned, the ethnic Vietnamese, they were all killed and this relates to my previous points about the paranoia of a Vietnamese invasion. They were treated as an enemy. There is some debate around the numbers here as well and the status of the Vietnamese in Cambodia even before the KR took power but I'll leave that as well.
The point is that in the Khmer Rouge Tribunals in 2014 the allegation of Genocide was brought against surviving members of the CPK. However - it was ONLY for those two categories of people, not for the Cambodian population as a whole.
So lets talk about using this word. Is it right to say 'The Cambodian Genocide'?
I would claim the stance that my former thesis supervisor David Chandler, as well as Historian/Journalist Philip Short take, which is that what happened in Cambodia, to the vast majority of people effected by the KR, was not genocide - but rather the appropriate term is 'Crimes Against Humanity'. It fits this perfectly.
If you want to say that 'the KR were genocidal', yeah... I guess you could. It should be noted that the surviving leaders Nuon Chea and Khieu Samphan were NOT convicted of the charge of genocide against the Cham and Vietnamese however. And this brings me to another of Short's points: The Khmer Rouge, the 'killing fields', that awful period of history happened predominantly to the Cambodians - not the Cham or the Vietnamese. 2 Million Cambodians died - the number of Chams who died probably around 100,000 - likewise the Vietnamese maybe only 20,000. So using the strict legal term of genocide to describe what happened to those two groups - to describe the entire period? That doesn't make much sense.
Nor does it make sense if you are using even a 'casual' definition of the word. Genocide in a very basic way entails the intent to destroy an entire group of people. The CPK didn't want to kill all the Cambodians - they wanted them to work and to build their utopian vision of society. The KR were callous above all else, they lacked any empathy and would kill you in a second if you went against them, but they didnt want to kill their whole population. Just a side note - the use of the term 'genocide' is highly politicised and an understanding of the motivations to use this phrase are interesting but maybe out of the scope of your question - but I am happy to answer any follow up questions you might have!
My sources include works by David Chandler, Ben Kiernan, Steve Heder, Alexander Hinton, Philip Short and Michael Vickery. I'm currently doing my thesis at Monash University and working on the podcast called 'in the shadows of utopia', which if you are interested can be found on itunes/acast or at www.shadowsofutopia.com