There was actually a major African presence in colonial Mexico. We don’t have exact figures but following some estimates Mexico received more than 200.000 African slaves during the colonial period. In the late 16th and early 17th centuries, New Spain (spanning modern-day Mexico, central America, but also parts of the Caribbean) had more black slaves than any other part of the Americas. After this, especially Brazil (far ahead) and then the Caribbean would become the most important destinations. Still, already by 1640 roughly a quarter million Africans had been forcibly brought to Spanish America and a similar number to Brazil.

So with African slavery a major force, your question has to do with how differently slavery developed in Mexico and, say British America or the Carribbean. This can be partly answered with chattel slavery being introduced at a later point, when Mexico (the earliest Spanish American possession) had already developed a different economic system – one especially focused on the important silver mines.

The other, maybe more important answer here is that in Mexico – in contrast to your other examples – Africans early on mixed with other groups. This meant that already by the 18th c. mixed descendants of Africans made up roughly 40% of the colonial population. By Mexican independence in the early 19th c. this trend had increased even more, and black slavery had virtually disappeared. This did not mean, of course, that other forms of forced labor for native and black people were not still in place.

I'll first look briefly at these larger economic differences and then turn to race relations in colonial Mexico. 20th century migrations are outside my field but I'll look at a few more current developments too. (heads up: I’m adapting from a few earlier answers of mine for this, so this’ll get a bit longer.)

Africans in early Spanish America

​ I think is an important question also because it ties to a larger topic that's still not so widely known: the major African presence in Latin America since the beginnings of colonisation. While scholarly interest has increased for decades, there are source problems with comparatively few documents of course written by African slaves, and with Spaniards showing relatively little interest in them (in writing, not for labor). Plus there are larger processes of social and political exclusion at play until today, of which more below.

In other regions outside Spanish America chattel slavery was introduced mostly later from the 18th onwards, with Portugal starting to focus more on Brazil in the mid colonial period. “Slave societies” even developed e.g. in northern Colombia and Brazil that were nearly apart from colonial society. So in that sense Colombia is actually quite a special case - I should just add that these regions would also keep a deeper African musical heritage, which would influence the development of some really great dance music like Cumbia in the later 20th c.!

In contrast, the earlier colonial centres of Mexico and Peru developed a different economic focus, with the silver mines providing the main income. There the extremely deadly labour (esp. in Potosí in the Andes) was mostly carried out by indigenous people, since African slaves were seen as "too expensive" for this (note the absurd logic here). Instead, many Africans did also work in less dangerous positions connected to the mines, e.g. in the mints.

We can say that the production of silver and its transport from Mexico was really the crown’s main concern in the region – with silver the motor of the Spanish empire’s economy. Partly because of this, agrigulture was of course an important sector esp. for Mexican production, but for the most part did not become a major source of export.

This connects also with the larger economic system of Spain: only the metropole (Spain) was allowed to trade with its overseas colonies. Officially, say Mexico and Peru should not trade between them. In the long term this meant that local economies were much more focused on export to Spain, and on producing primary products for local consumption rather than export. Some experts say this stifled Latin American economies in the longer run, which is a different question though.

Due to these different economic systems, Africans and their descendants in most of Spanish America had quite a different status from those in Brazil, the British and French Carribbean, and the later U.S. Africans carried out a variety of tasks (of which more below), would often intermarry with native women, and in many cases could buy their freedom.

According to Restall & Lane, in the mid-colonial period in most of Spanish America, more than 50% of Africans and mulattoes (so mixed African and European or indigenous) were freed, through manumission or other means. This is in contrast e.g. with Brazil with a much lower rate of freed slaves, where manumission was more complicated. This decrease in Spanish American slavery also coincides with the British increasingly taking over the American slave trade after 1640 from the Portugues - leading to a major increase in slaves forcibly transported from Africa.

Restall & Lane make another helpful distinction for your question: between "slave societies" of mass slavery on plantation, ranches and in mines (so incl. chattel slavery); and on the other hand "societies with slaves" where auxiliary slaves took up a variety of tasks. In the latter case

economic and social relations did not revolve around slavery, individual slaveholders owned small numbers of slaves, manumission was possible (if not encouraged), and slave revolts and maroon communities were rare or nonexistent.

With some exceptions, Spanish America then had mostly such societies with slaves, in contrast to the examples you mention. Economic history is not exactly my specialty, so in the following I want to look more in detail at race relations in Mexico, and how Africans integrated into colonial society – probably the main influence on the petering out of official African slavery in the region - and what tasks slavery comprised there.