This isn’t going to be the in-depth treatise about the philosophical and liturgical differences between babalawo and olorisha (in Lukumi). I don’t have the energy for that post while I am on the road. But this is just to give newbies a cheat-sheet as the terms can get confusing.
First off, a babalawo is a (heterosexual) male priest of the orisha Orunmila (AKA Orunla/Orula/Ifa) who are expert diviners of the system of Ifa [you see how the various overlapping in names for different but related things can be a tad obfuscating to the regular Jose? So, babalawos tend and administer to anyone and everyone. The kings of Yorubaland have a cadre of babalawos to consult for stately matters. You, I, or anyone can have a consultation with a babalawo and he will divine using a couple of different methods at his disposal to obtain an odu of which there are 256 and then give you advice, prescriptions, proscriptions and all sorts of help. A babalawo will and can initiate other babalawos who are (heterosexual) men. For those who are not destined to become a babalawo can receive the one hand of Ifa or a person’s own consecrated Orunla. It is called Awo Ifa Kan/awofakan if the person is a man and Ikofa if a woman is receiving it. The recipients now have their personal Orunmila to worship, they will have an odu from the ceremony, and it is in this ceremony that many learn who their guardian orisha is. The babalawo can also confer other orishas, such as Eshu and the warriors and there are orishas and other deities that babalawos receive. Depending on the practices of the lineage, some babalawos give other orishas such as Oduduwa, Osayin and so on. The signature colours of the babalawo are green and yellow and they wear a bracelet and a necklace in these colours which are also given to devotees for protection from Iku/death.
The necklace and bracelet (ide) of Orunmila
So, if babalawos worship the orisha Orunmila and only initiate other babalawos what about all the other orishas? Olorisha is the gender-neutral term for a santer0 (male priest of the orishas) and santera (female priest of the orishas), often combined as santer@.
Santeros are priests and children of any of the orishas except Orunmila such as Elegua, Ogun, Oshosi, Oshun, Obatala, Shango, Oya, and Yemaya as well as all the rarer ones like Inle and Orisha Oko. A priest of any one of these orishas can generally initiate children of other orishas (the exceptions here are Oya with children of Shango and Yemaya, and a few other exceptions). So, if I am a priest of Oshun and you found out in your Awofaka/Ikofa that you are a child of Yemaya who needs to be initiated, I can initiate you. The bead colours of the orishas differ greatly and each orisha has his or her signature colours. An olorisha will receive during their multi-stranded bracelet/ide in the colours of their guardian orisha to designate their status as a priest and who their guardian orisha is.
Some olorishas/santeros find out that they have a “path to Ifa” which means that one day they can be initiated as babalawo. A person can first become an olorisha and then a babalawo, and such a person is given the title Oluwo. A babalawo can not become an olorisha if he did not do so before “passing to Ifa.”
I hope this short explanation hopes to clear some of the different words used for priests in Lukumi.