The Religious Emblem Counselor is trained and approved for that role by the respective religious organization’s committee on scouting. E.g.,the local diocesan Catholic committee on scouting, or the Jewish committee on scouting, etc. This is the person who guides scouts at the Scouts BSA / Venturing level through their religious emblems. So, a Catholic will be a counselor for Catholic Scouts, a Muslim for Muslim scouts, etc.
The Unit Religious Emblem Coordinator is the person in the unit responsible for promoting religious emblems, connecting scouts to the appropriate counselors, and encouraging people to get the appropriate training and approval from their respective religious committee on scouting to be counselors. Think of it is parallel to the unit merit badge coordinator. This person would work with the chaplain if you have one, of course, but does not need to be a religious professional or minister, nor do they need to be any particular religious affiliation - they promote all religious emblems, of all faiths.
The District Religious Emblem Coordinator would be part of the COuncil’s religious relationships committee, presumably, and would coordinate with the unit religious emblems coordinators, the various religious committees on scouting, and the chaplains to promote religious emblems district wide, and especially in areas where each unit might not have their own list of counselors, the district can maintain and support this (also parallel to merit badge coordinator).
Chaplains are ministers, religious leaders, who would also support religious emblems programs, but work for the overall spiritual well-being of scouts, promoting interfaith opportunities, and if relevant, religious scouting events related to the charter org.
The counselor role has been around a long time, but i don’t know that it was always acknowledged as a registered position since it was determined by the religious committees.
The coordinator roles are relatively new.