I’m asking specifically about the Europeans during their colonial period. My guess is it just sort of happened organically. Africa was on its way to the Western Hemisphere. They could be obtained cheaply and easily, and they filled the need for manual labor.
But there was a period when these empires had many subjected peoples they saw as inferiors. Native Americans, Indians, Pacific Islanders, etc. Why were some people colonized, or pushed off their land, instead of being enslaved? If they were already transplanting huge numbers of people one way, why not the other?
Europeans used practically everybody as slaves, but I will write specifically about slavery in Australia.
From the earliest days of European colonisation, the invaders sought to have Indigenous Australians do their labour, for several reasons: convicts could be quite lazy and rebellious, and demanded payment after certain times of the day, and fair treatment; ideas of racial hierarchy, where coloured labour performed all basic tasks; and the idea of the civilizing mission, where work would teach savage and immoral people to become proper Christian men and women. In the early years of settlement, abuses of Aboriginal people were largely kept in check by the military authorities in the vicinity of Sydney, but once the frontiers spread to beyond the Blue Mountains and squatters rushed ahead of legal settlement, it was impossible to police. Putting aside sexual slavery of Indigenous women and children, labour could be negotiated with the tribe with the provision of gifts, but more often than not it was forced. This usually led to conflict and violence, where tribal justice demanded the spearing of the guilty settler, and frontier justice required 'teaching the blacks a lesson' by having a posse indiscriminately shoot a number of natives, regardless of whether or not they were even related to the 'guilty' party. This led to all out war, where settlers called in the military. Massacres became significantly worse when horses and rifles reached the hands of settlers on the frontiers, and when the military handed policing responsibilities to civilians.
Labour was always in high demand in Australia, and on the frontiers in particular. Indigenous women and children were also kidnapped by sealers and whalers (again, for sex and work), and men forced to act as guides, diplomats/translators, stockmen, laborers, porters, trackers and other jobs. John Hirst writes that when forced to work, Aboriginal men usually either simply walked off, or saw themselves like European gentlemen and demanded to have others (like convicts) work for them. The traditional Indigenous lifestyle in temperate Australia was fairly relaxed outside of war or drought - women usually did the majority of the work, while men hunted.
In the later 19th century, as European settlement spread north, frontier slavery significantly worsened. In the arid and tropical regions across the north, white settlers (especially women) were incredibly rare, and most white men were squatter pastoralists who relied on 'coloured' labour. In Queensland this was mostly 'Kanaka' indentured labourers from the Pacific Islands, usually Melanesians, who were tricked or outright forced into working on the sugar cane fields. Slave labour was ubiquitous in the pastoral industry, especially in northern WA and the NT, and WA pearling also relied heavily on slave and indentured labour, not just of Aboriginals, but also of Japanese, Chinese and Malay migrants. In the run up to the federation of the colonies into the Commonwealth of Australia, the far wealthier, populous, progressive and 'whiter' states of NSW and Victoria pressured Queensland and WA into deporting their foreign labour, to appease the unions and to bring about racial purity in line with the ideals of White Australia - rural northerners claimed their businesses were unprofitable without forced labour, but they were forced to bow to southern urban demands.
Again, in regard to Indigenous Australians in the north, sexual slavery was also incredibly widespread, with women and children forced into domestic servitude. People openly bought and sold slaves, and knew which slaves 'belonged' to which pearling ship, household or cattle station. Escaping slaves were shot, and resistance or tribal justice usually led to massacres that 'put the blacks back in their place', the last such massacre being in 1928.
These conditions were known by authorities but heavily denied, and protests from missionaries or humanitarians travelling north from southern capitals were usually ignored, inquiries usually leading nowhere. Protests generally got more response from London than from the colonial capitals. These conditions continued on until at least the 1940s, despite growing pressure from urban Australia and overseas to treat Aboriginal Australians humanely. Australians feared negative publicity in Britain and elsewhere, and negative comparisons between themselves and countries like apartheid South Africa. When the government finally mandated that all Aboriginal pastoral workers be paid wages instead of in food and board (which were not legally enforced and there were many cases of workers starving to death), pastoralists simply turned there workers out. Having no where to go, many met miserable ends, whereas others migrated to southern cities far from their country.
'De-tribalised' or 'half-caste' Aboriginals - Indigenous people with mixed ancestry who lived in long-settled territory - were treated differently. Prior to Federation (1901), they usually lived on reservations under the protection of the Chief Protector of Aborigines, in missions, or in camps on the outskirts of towns (or near swamps, hilly bushland and other undesirable land in cities). On missions and reservations they were treated much like on the stations in regards to labour, the main difference being that they were physically safe, but culturally required to assimilate (genocide by another name). They were given cramped and poor quality quarters, no medical attention, meagre rations that lacked nutrition and were forced to abandon language and tribal ties. Fringe-dwellers might get sponsorship from local landowners - some in my city worked on the wineries - but most were usually hounded/raided by the authorities, told to assimilate but not welcome to do so. All Aboriginals were monitored by the Chief Protector of Aborigines, and had to work, and were tied to their bosses, needing to seek permission to travel or quit work. Most were not paid, their pay instead going to the state, their employer or the church, to be held in trust - you had to write a letter to the Chief Protector to access your money, and it quit often went missing. In an attempt at speeding up assimilation, several colonial/state governments legislated the removal of mixed ancestry (half-caste) children to missions to be trained as domestic servants for white families. This caused massive upheaval - tribes were wiped out as entire generations of children were stolen and scattered across the state, some never seeing their families again. Both stolen wages/indentured servitude and the theft of children only stopped in the 70s (perhaps longer in conservative North Queensland), although many argue that children continue to be stolen today in the form of youth detention and foster care.
Australia also had questionable practices in its colony of Papua New Guinea, but I know very little about this. Officially, slavery has never existed in Australia, and most Australians deny it ever did occur. Compensation for historic stolen wages is a secondary political concern of some Indigenous groups, with land rights, health and police brutality usually being more prominent concerns.
u/AbandoningAll has also answered this question extremely well, I would highly recommend giving it a read too.
My main sources:
Henry Reynold's The Whispering In Our Heart, which covers the lion's share of this, and is an incredibly powerful and heart-breaking read. It is about white humanitarians who attempted to address settler abuse of Indigenous Australians.
John Hirst's Australian History in Seven Questions, specifically the end of Chapter One, where it discusses Indigenous work in agriculture.
John Connor's Australian Frontier Wars
The First Australians (book or tv series)