I would imagine colonization happened for economic gain with the colonists benefiting. The colonized population were likely still governed by the locals who were controlled by the colonizers.
For example, India was a colony of Britain. All trade was diverted to Britain to benefit them. The great famine of bengal for example was because farmers had to grow and send cotton to England rather than grow food for Indians. The economic activities were controlled by the colonizers armed forces.
The British colonized India. The Moghals invaded India. Alexander, The Great...for example..tried to invade India, but had to retreat. It’s usually done with armies vs colonizations that is through trade.
An invasion is when a military moved in and took over the government. The invaded country became the de facto territory of the invaders. And the invaded people have to live by the rule of the invaders. Example: Georgia was invaded by mongols and the Turks and then Russia. Each time, it became part of the other’s empire.
The US was colonized with entire family units being uprooted and moved, and little cultural and marriage intermingling, sometimes by law.
Mexico and Central/South America instead starting as a military venture with mostly men raping/“marrying” the native women and having children that way.
I suppose the main difference is that the colonization of the US was an invasion that was so successful that native Americans living there before were almost exterminated(being today less than 1% of the US population) and as a result nobody cares about them anymore.
Usually invaders, like Alexander the Great, Tariq ibn Ziyad , Kublai Kan, Hernán Cortés or Napoleon will kill opposition(mostly males) but leave women and children and men who don't oppose them.
That means most of the society remains the same after the invaders take control of power, and grant special privileges to themselves, like owning the best land or having sex with the local women.
In the US, they never mixed with local population, they just expelled them of fertile soil until they died from starvation, illnesses or fights.
It’s not An Invasion per se...America was colonized. The impact of invasions are different in history’s timeline.
Regardess, those who reached American shores were the Puritans and their ilk anyways.