A word with several senses
At its narrowest, irmandade names the kinship between brothers or sisters; the related word fraternidade, from the Latin frater ("brother"), covers the broader sense of solidarity among people who are not literally kin. In Catholic usage, an irmandade is often a lay confraternity organized around devotion to a particular saint or title of Mary — the Irmandade de Nossa Senhora do Carmo is one example — combining religious practice with mutual support among its members.
The Catholic Church in Brazil has drawn on this same idea of fraternidade in its annual Campanha da Fraternidade, a Lenten program of reflection on a chosen social theme — among them, over the decades, hunger, unemployment, and public health.
Black brotherhoods and religious syncretism
In 19th-century Brazil, Black Catholics were barred from worshipping alongside white congregations, which led to the formation of separate irmandades negras (Black brotherhoods). These became spaces where Catholic devotion mixed with Candomblé, an Afro-Brazilian religion, and other traditions of African origin — a meeting point historians point to as an early site of Afro-Brazilian religious syncretism. Beyond their religious role, these brotherhoods also functioned as networks of social support within Black communities.
Further
Irmandade is the institutional word before it is the affectionate one. In Portuguese it names a lay confraternity organised on religious precepts — Irmandade de Nossa Senhora do Carmo, and the like — a body with membership and obligations. Fraternidade is the feeling rather than the body: solidarity, cooperation, love of neighbour. Daime churches use both, and the distinction is worth keeping, because one describes how a church is organised and the other how its members are meant to treat one another.