This is my favourite way of answering questions here and it definitely applies to this one: "yes...sort of..."

Let me start off with this quote:

“In point of time, the Crusades are the opening chapter of European expansion and foreshadow all later colonial movements.” (Prawer, The Crusaders’ Kingdom, pg. 469)

That's a pretty bold statement, and whether or not it's true is a big issue in the crusades. Whether it's true or not, colonization during the crusades certainly wasn’t much like European colonization of the Americas in the early modern period. Early modern colonization was largely state-run or at least state-sponsored with specific companies organizing voyages and settlements. But that requires, well, a “state” in the more modern sense. Medieval European kingdoms weren’t really centralized states like that, so they had no way to organize a colony.

The crusader states were a bit more like ancient Greek or Roman colonization, where individuals or small groups set off on their own around the Mediterranean or the Black Sea. They were connected to the “mother city” (literally their metropolis) but they mostly fended for themselves and developed on their own.

You noted that European nations shipped boat-loads of people to their colonies, but there was no way for a medieval kingdom to do that. They were able to create new settlements in their own countries - there were lots of medieval “new towns” in France and England and Spain, but that’s not the same as sending a bunch of people over the sea to a place where the environment and the language and customs were entirely different.

Colonization in the early modern period also depended on a different worldview - Europeans could colonize places like North and South America, and later Australia, because those continents weren’t part of the ancient conception of the world (Europe/Asia/Africa). Even though there were people living there, they weren’t “civilized” people. It was a “new world” and “terra nullius” - land owned by nobody. The crusader states were established in a place that was already part of their own civilization. By that point, the Near East was also far more advanced than Europe, so they weren’t settling in a "primitive" area.

After the First Crusade, the crusaders mostly lived in cities and towns and villages that had already existed for hundreds or even thousands of years. The population that they conquered probably wasn’t even majority Muslim. There were lots of eastern Christians there, and the Latin Catholic crusaders tended to live wherever they lived.

However, all that being said, there definitely were “colonies” in the crusader states. The crusaders occasionally created “new towns”, like in England or France or Spain. One example of this is Bethgibelin, which the crusaders founded around 1136. This is a generation or two after the First Crusade, so there were people who were born and grew up in a crusader society, and some of them helped create the new settlement at Bethgibelin. They built a castle there, which was granted to the Knights Hospitaller.

Countries weren’t able to organize colonies in the Middle Ages, but the military orders like the Hospitallers and the Templars actually could! They were kind of like multinational corporations, so they did have the resources and the connections to organize a colony. But the colony didn't have any connection to one specific country, like early modern colonies did. The settlers at Bethgibelin came from:

"...Auvergne, Gascony, Flanders, Lombardy and Catalonia. Generally, the largest number of European settlers...were from the central, southern and western parts of France, and a few also from northern Spain and regions in Italy. In Bethgibelin the other settlers were from nearby Latin villages..." (Nader, pg. 94)

So it was possible to bring colonists from Europe, and a European society did exist in the crusader states, but it wasn’t due to the effort of specific nation and people from different parts of Europe all lived together, unlike early modern colonialism.

The other exception to this is the Italian city-states like Venice, Genoa, and Pisa. They had their own quarters in some of the cities of the crusader states, like in Acre or Tyre. They were trading colonies, full of merchants, and they did have close contact with the political leaders of their cities back home. The rulers of Venice, for example, sent out officials to report back on the status of the merchants in their merchant quarters. That’s more like the ancient Greek city-states sending out colonies though. The Venetians and the others didn’t really send out families to settle there. They were mostly concerned with making as much money as possible through trade.

I should also point out that this is debated among modern historians, so it gets into questions of historiography, not just history...I hope this is not too dry and technical, but what I mean by that is, sometimes the crusader states are described as colonies or proto-colonies, but the reasons for that may depend on the (conscious or unconscious) beliefs of modern historians.

For example, maybe the most important historian of crusader society was the Israeli historian Joshua Prawer, the source of the first quote at the top of this answer. He often wrote about the crusader states as an early form of colonialism, similar to but not exactly the same as what developed a few hundred years later in the Americas. But was he also thinking of the establishment of modern Israel? He was from Europe himself and was involved in the early settlement of Israel. Did he try to depict the crusades in the same way, to make the creation of Israel more relatable and acceptable?

The same goes for the opposite point of view. If modern historians depict the crusades as an unjustified outburst of violence against a superior culture, which temporarily occupied the Near East before being defeated, are they *also* thinking of events in the modern Near East? So there’s a little bit of a debate about this, and it gets into questions of Zionism and Marxism and modern political disputes.

In summary: yes the crusaders did have colonies and colonists, but there was no such thing as colonialism in the modern sense. Whether the crusades were an early form of European colonialism is a matter of some debate (but they probably weren’t).

Sources:

Prawer is well-represented here since he’s still very important and influential. For different views on what the crusaders were doing, check out the works by Marwan Nader and Ronnie Ellenblum:

Joshua Prawer, The Crusaders' Kingdom: European Colonialism in the Middle Ages (Praeger, 1972, repr. Phoenix Press, 2001)

Joshua Prawer, “Social classes in the Crusader States: The ‘Minorities’,” and “Social classes in the Crusader States: the Franks,”in A History of the Crusades, vol. V: The Impact of the Crusades on the Near East (University of Wisconsin Press, 1985)

Joshua Prawer, "Colonization activities in the Latin Kingdom of Jerusalem," in Revue belge de Philologie et d'Histoire 29 (1951) pg. 1063-1118

Ronnie Ellenblum, “Colonization activities in the Frankish east: The example of Castellum Regis (Mi'ilya)”, in The English Historical Review 111 (1996), pg. 104-122

Ronnie Ellenblum, Frankish Rural Settlement in the Latin Kingdom of Jerusalem (Cambridge University Press, 1998)

Marwan Nader, Burgesses and Burgess Law in the Latin Kingdoms of Jerusalem and Cyprus (1099-1325) (Ashgate, 2006)

Piers D. Mitchell and Andrew R. Millard, “Migration to the medieval Middle East with the Crusades”, in American Journal of Physical Anthropology (2009), pg. 518-525