The clearest way to place a babalorisha is against a babalawo, because the two are constantly confused outside the tradition. A babalawo is initiated to Ifa. His subject is the corpus of 256 Odu, his instrument is the tray or the chain, and his work is divination. A babalorisha is initiated to one orisha, Sango or Osun or Obatala or another, and his work is the cult of that orisha: its shrine, its offerings, its festivals, and the initiation of others into it.
The title means father of the orisha, and the parentage is the load bearing part. Someone initiated by a babalorisha is his child in the religion, and remains so; the house is a lineage and it is spoken of in kinship terms throughout. Seniority runs by initiation date rather than by age, so a person of sixty initiated last year is junior to a person of thirty initiated at twelve.
What the initiation consists of is closed, and is not described here or anywhere else in this atlas. What can be said is that it is not ordination in the sense a reader from a Christian or Islamic background will expect: there is no seminary, no examining body and no institution that can revoke it. Authority comes from the lineage and from the recognition of other priests, which is exactly why disputes in the tradition are so often disputes about who initiated whom.