The big difference is how many people come to the land being colonized or conquered. If it is not that many and they are mostly military, then it is conquest and the relatively small number of people run the government, often by using a puppet ruler.
Colonization is when large numbers of people come over and plan to live there. They start farms and businesses and have children and in general make their lives there. Colonization is easier if the land is relatively empty due to being thinly populated, or if diseases have wiped out a lot of the original inhabitants.
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