How was the term kulak itself used by peasants? Was the division of society between peasants and kulaks accurate?
The exact definition of what constitutes a kulak (translated from the Russian word meaning fist) is presented by Lenin in a 1919 essay entitled Answer to a Peasant's Question:
[T]he kulaks [are] rich peasants who exploit the labour of others, either hiring them for work, or lending money at interest, and so forth. This group supports the landowners and capitalists, the enemies of the Soviet power. [1]
What this actually means in application is that in 1861, when Emperor Aleksandr II emancipated the serfs of Russia (which was the rough Russian analog of chattel slavery-- you are not free, your children are not free, you can be bought and sold, so can they), some of these people were able to secure land ownership for themselves. How they were able to do that varied:
With respect to the first bullet point, these deals were organized between the land-owning nobles and their now-former serfs. There was no government involvement in these transactions and many of them proved to be fraudulent or at the very least misleading. As for the latter, the deal was that these former serfs were granted land in exchange for a portion of their harvest each year, paid to the government, for some allotted period of time, which eventually culminated in their outright ownership of that land. Milyutin and Stolypin were interested in keeping farmers on their land, tilling it as they had been before their emancipation.
If, suddenly, the bulk of Russian peasants moved in to the cities (which many did anyway) seeking better conditions and giving up the life of a peasant farmer, the Russian Empire would be exposed to an even greater risk of famine than it already was-- both Milyutin and Stolypin recognized this and sought to incentivize peasants to remain on their farms. As a side note, this migration of the peasant classes to the cities is what Stalin used to justify his forced collectivization of the Russian peasantry some 20 years later-- which was effectively the re-institution of slavery in Russia. [3]
After some time had elapsed, many of these peasants were able to secure legitimate ownership over modest tracts of land. Sometimes these people hired other former peasants to work their land alongside them, but it's important to emphasize here alongside them. These people were not slave-owners. Their workers were paid, housed, and fed in most cases. Others lent tools and livestock to smaller landowners nearby for a profit. I'm not going to sit here and tell you there was no such thing as the 'evil kulak' Lenin and then Stalin vilified and then liquidated, who ruled over their newfound demesne with an iron fist and offered low-quality conditions to their poor peasant laborers. Cycles of violence tell us that those who are violently oppressed can sometimes turn into violent oppressors themselves given the opportunity, but it was nowhere near the norm-- as Lenin and Stalin tried to present it. Some people who came to be described as kulaks later would likewise bribe imperial officials to avoid conscription to the frontlines during the First World War, but to suggest that this practice was widespread among all of the people whom the Bolsheviks eventually sought to murder and/or from whom they violently expropriated land, grain, or other resources is complete nonsense.
The nascent Russian Soviet Federative Socialist Republic (RSFSR) required control over the grain supplies to feed their burgeoning state, which almost exclusively occupied industrial cityscape that was completely devoid of farmland and therefore, food. The rural Russians who either supported the Emperor over the Bolsheviks outright (and therefore refused to provide their grain to the latter in order to feed their armies and polity), or simply opposed both (and therefore refused to provide their grain to either in order to feed their armies and polity) had to be coerced one way or another, it wasn't long before the Bolsheviks (and frankly the Imperial Army as well) just resorted to violence.
Marxists.org makes the following unsourced claim:
By 1917, the success of kulaks cannot be seen more clearly than in the amount of land they owned: over nine-tenths of Russia's arable land. [4]
Stephen Kotkin's biography of Stalin presents a significantly smaller figure, but says explicitly that attempting to assign a concrete value to this metric is nothing more than an estimation in the best case. [5] I'd wager that Marxists.org is likely including the noble classes who owned land as well as an ambiguous definition of kulaks in the figure above which should make it invalid for obvious reasons.
How was the term used by the peasantry itself? Unfortunately the vast majority of these people were illiterate so we don't have any sources (that I'm aware of) concerning how the peasantry viewed the kulaks-- written by the peasantry themselves. [6] There were certainly massacres of people labeled kulaks by peasants though, which I think helps to elucidate how these people were thought of amongst their peers. Such practices were encouraged or orchestrated outright by the Bolsheviks but I think it would unfair to say this was done out of anything more than self-interest. The Bolsheviks encouraged the worst impulses in people quite often, and strong-armed robbery was the form that usually took.
Consider Stalin's writing in Concerning the Policy of the Elimination of the Kulaks as a Class of People (1930):
[T]he policy of eliminating the kulaks as a class could not have fallen from the skies. The way for it was prepared by the entire preceding period of restricting, and hence of ousting, the capitalist elements in the countryside. [7]
There was never any doubt about what the fate of those labeled kulaks was to be, the only ambiguity lay in whom the word described, and that umbrella eventually covered far more than just exploitive land-owners who oppressed the proletariat via pyramid scheme lending and oppressive employment conditions.
Sources and Further Reading