Africans in Latin America often maintained particular spiritual practices back to the 1500s; however, the particular African Diaspora religions really started to crystallize in the 19th century.

This is in large part because of the massive influx of enslaved Africans during that period. If you look at these estimates, roughly 40% of all slaves transported to Brazil and 80% of all slaves transported to Spanish America (mainly the Caribbean) arrived between 1800 - 1875. This massively reinforced the African character of many of the African communities in the region.

To start with - the religions did originate along regional lines. There are a few main families:

Yoruba Religion: This evolved into modern Lucumí/Santería in Cuba and as Candomblé and Umbanda in Brazil. Santería and Umbanda are both also influenced by 19th century Spiritism. There are a lot of other minor sects of Yoruba religion in various countries - Yoruba religion is by far the most popular of the African Diaspora variants.

Kongo Religion: This became modern Palo Mayombé/Palo Monte in Cuba. FWIW 19th century Brazil also had Kongo religion practitioners, but today that's been largely overshadowed by the various Yoruba-based religions.

Calabar Religion: This became modern Abakuá in Cuba, and is unique in that it exists as secretive lodges with initiation ceremonies. Interestingly, the Spanish unintentionally spread the religion when they deported Cuban practitioners to their African colonies.

In terms of beliefs, they all emphasized the powerful role of ancestors and spirits in human life, they all had some form of guarded sacred knowledge.

This is immediately complicated by the mixing of different groups of people in Latin America. Not only did Afro-Latin Americans sometimes mix and match between different sects, but Europeans also sometimes participated. Additionally, the these religions were also variously influenced by Catholicism, Spiritism, Amerindian beliefs, and at times each other as well.

The broad unique features of each religious family are:

Yoruba: Yoruba religions had an extensive pantheon with deities such as Chango, Ogun, Yemaya. A lot of Santería is based around divinization, identifying the spiritual forces active in one's life, and developing the relationship with a particular deity. FWIW, the name "Santería" originated because practitioners associated deities with the images of Christian saints.

Kongo: Kongo religion had a creator god who is relatively distant from the present world. Instead, humans negotiate their relationship with a variety of spirits as nkisi (which refers to both the spirit itself as well as any cult figures or ritual pots in which the spirit resides). This can involve collecting various ritual objects to perform rites to the nkisi

Calabar: This is based around the Ekpe cult a.k.a. the Leopard Society of Calabar. This is vaguely similar to Yoruba religion, except this is based around a cell-like structure of secretive initiates.

In terms of conflict, I am not aware of a lot of direct competition. These were not particularly missionary religions, and in any case a lot of Latin Americans did (and still do) participate in diverse spiritual practices based on what appears to be beneficial.

The main exception is the various Abakuá lodges fighting with each other in 19th century Cuba, although this had more to do with the lodges competing for dock monopolies than anything particularly religious.

Sources:

Afro-Latin America 1800-2000 by George Reid Andrews

Conversion of a Continent: Contemporary Religious Change in Latin America by Edward Cleary

The Social Significance and Implications of the Ekpe Shrine In Calabar, Nigeria by Offiong Offiong Asuquo

The Kongo Rule: The Palo Monte Mayombe Wisdom Society by Lydia Cabrera