The way England/UK colonized is different from France from Belgium from Spain, but in what distinctive ways and how did that affect the colonized and the colonizers themselves afterward?
This is of course a huge question that fills books. In order to show one approach to this that I've found helpful, I'll first draw on Jürgen Osterhammel's classification of colonialism. Second I'll look at some ways of comparing Spanish colonialism (which I'm more familiar with) and other forms of colonialism. This is necessarily informed and limited by my own approach, so I'm hoping others studying other forms of colonial empires can add to it.
Caveats
I'll have to start off with a few caveats regarding your question. First off: How useful is it to actually look at differences between various European colonial empires (Spanish vs. British vs. French etc.)? Apart from the huge span of such a question, there are other problems. In some cases looking at specific national "characteristics" of empires goes back to earlier, more national ways of writing history (both in European and post-colonial states). Moreover, building on Wallerstein, Osterhammel notes that there are various parallels in the development of the colonial empires. This includes the moment when the first conquistadors and other soldiers are usually replaced or controlled by administrators. This is shown quite clearly in the early Spanish America, where the conquistadors' struggles to hold large encomiendas (rights to native labor) where quelled by the Spanish Crown in favor of colonial administrations.
What is more, the different colonial empires were built on various nationalities, and often pan-European - including the ship troops, missionaries and soldiers. Again, looking at the Spanish empire we get people from Spain's Italian, Dutch and other possessions moving to Spanish America (as shown by Henry Kamen and others). Similarly, the Carribbean planter class of the 18th c. came from various parts of Europe.
Most importantly, focusing solely on specific European nationalities excludes the experiences of the colonized. These would often highlight continuities, often changing colonial rulers - e.g. in South and South East Asia. Osterhammel argues thath the origin of the colonizers was, for the colonized, not unimportart but of secondary importance. From colonial Mexico I've read about native authors often giving much less importance to the Spanish conquests than the Spaniards would, positing them as only one in a larger series of conquests running from pre-colonial to colonial times.
Jürgen Osterhammel thus argues that a non-Eurocentric colonial historiography should focus not so much on the colonial politics of the European powers, but rather on the rise and fall of specific colonial societies, or social forms - with a stronger focus on the subjects, and interactions between all participants (colonisers and colonized). Because of this there can not be one "history of colonialism", but different histories of forms of colonialims.
A definition
Before we're taking a look at Osterhammel's ideas for classifiying forms of colonies, his definition of colony gives a good background. Note that I'm drawing on his "Kolonialismus: Geschichte, Formen, Folgen" which has been translated into English:
A colony is a newly formed political construct, created through invasion (conquest and/or settler colonisation) and building on pre-colonial conditions. Its foreign dignitaries are in continuous dependancy relations to a far away "motherland" or imperial centres, which raises exclusive claims of ownership to the colony. [my transl.]
We should note that "colony" and "colonisation" are not one and the same - there can be colonisation without the creation of colonies; and vice versa, colonies can be created merely through military conquest.
A classification
Osterhammel proposes a classification of colonies that were formed in modern times through the expansion of the European states, the USA and Japan. As noted, these do not mean necessarily a distinction between specific colonial empires, but rather between forms of colonies - some of them shared by the same empire.
1) Dominions ("Beherrschungskolonien")
These were mostly the result of military conquest, often after prolonged phases of contact. They served economic extraction (e.g. through monopolies, tributes), and the strategic protection of imperial policies. Dominions would have a relative small colonial presence, esp. through civil bureaucrats who would return "home" after their service, through soldiers and salesmen - but not through soldiers. The governemt was led autocratically through the metropole - through the governor system -, with elements of paternalist care for the native populations.
Examples would include British India, Indochina (Fr.), Egypt (Br.), Togo (Ger.), Philippines (Am.), and Taiwan (Jap.). A variant of this was Spanish America, were European migration led to a mixed, urban society dominated by a creole minority - I'll talk about this some more in the 2nd part below.
2) Foothold colonies ("Stützpunktkolonien")
These were formed as a result of naval actions. They served the indirect commerical exploitation of a hinterland, or as an aid for the logistics of develpong maritime power over formally independent states ("canon boat policy").
Examples include Molucco (Port.), Batavia (Dutch), Hongkong, Singapore, Aden (al Br.), Shanghai (international). I'd add here that at least with Dutch colonisation it's often mentioned that it was more focused on exploiting existing trade networks rather than on evangelisation - a marked difference to e.g. Iberian colonisation in the same regions.
3) Settler colonies ("Siedlungskolonien")
These were formed as a result of colonial processes aided by the military . They were supposed to lead the use of cheap lands and cheap (foreign) labout; and make possible the socio-cultural practices of minorieties that were questioned and/or persecuted in the motherland. Colonial presence was primarily through permanent settlers and farmers. Early on this would include the beginnings of self-governance of "white" colonists while violating the rights and interest of the indigenous populations.
Here Osterhammel lists 3 variants:
a) The "New English" type: Displacement and partial desctruction of the native populace - as in the New English colonies, Canada (fr./br.), and Australia.
b) "African" type: Economic dependancy from native labour - e.g. in French Algeria, South Rhodesia (Br.) and South Africa.
c) "Carribbean" type: The import of foreign slaves for labout - in the French & British Carribbean, as well as Brazil (Port.).
To conclude this part, I would add that to me Osterhammel's classification is useful in that it shows larger trends of colonialism that were common to different regions - often regardless of which European nation/empire held control over the specific region (it's also more complex than what I've discusses here, so I'd recommend the book to those interested). Then again, I find it important to look more closely at the regions themselves to distinguish more clearly between differences and parallels between diffierent colonial approaches.
Last but not least, it's extremely important not to see colonial expansion solely from a European perspective. For many indigenous people colonisation was one among many influences on their lives - a distruptive one for sure, but often not the dominating one. What is more, throughout human history there were many non-European empires that would often clash or collaborate in different ways with the European colonial powers. In many ways, especially "informal" colonialism continues to this day through less obvious, neo-colonial approaches of exerting control.
This got me thinking so I hope it's cool to add to your question OP :) I heard the Iberian, Belgian and British were brutal towards the natives but how were the French/Dutch in comparison and was the colonization of America more brutal than that of Asia/Africa/Australia?
Amazing response, muito muito obrigado!