If two priests celebrate Mass, they are said to concelebrate.
If a priest joins another faith’s religious leader (minister, pastor, imam, rabbi, parson, preacher, etc.) in a religious observance, is it also considered concelebration? Or is concelebration reserved as a reference solely for a Mass or other Catholic service?
Concelebrating is really a term related to the Eucharist because of the underlying theology of the priesthood and theology of the Eucharistic celebration. In that moment, we are simultaneously acting
in persona Christi Capitis
I have had a few occasions at which I have presided at a baptism of a baby and another priest will be present, for reason of an association of some sort with the parents, godparents or so forth. I would invite the priest to vest and to join me at my side in the narthex, baptistery, and sanctuary. He would sign the child with me and the parents and godparents. He would read the Gospel and pray the litany. Having done the homily, I would do the rite of baptism itself. Then I would ask him to do the rites after baptism…the post baptismal anointing, bestowal of the white garment, and the
Lumen Christi. It was not concelebrating theologically since we do not simultaneously confect a sacrament but I would imagine that was the term likely used to informally describe what happened by those attending who were laity.
The rites make provision for the Presider to associate with himself others priests who are present in the bestowal of a sacrament on multiple persons – Confirmation, Penance, and Anointing of the Sick most notably – but here we are dealing with multiple ministers imparting a sacrament individually to distinct individuals in association with the one who presides at the rite of conferring the sacrament.
In services that are ecumenical above all but also applicable for inter-religious events, the normative terms would be co-officiate/co-officiant and co-preside/co-presider. These are the terms relative to Pope Francis and Bishop Younan of the Lutheran World Federation who will co-officiate at a Service of Common Prayer in Lund, Sweden, next month to inaugurate the Joint Lutheran-Catholic commemoration of the 500th anniversary of the Reformation.
There is a special Service of Common Prayer, promulgated and published by the Holy See and by the Lutheran World Federation, for use all over the world since Catholic Bishops and Priests and Lutheran Clerics will locally be hosting these joint commemorations at which a cleric from each will co-preside and impart together the final blessing at the dismissal. The agreed upon terms used for the Lutheran Cleric and the Catholic Cleric who will together co-officiate these Services of Common Prayer is “Presider I” and “Presider II”
In cases where I have been formally invited or formally sent to be present in some official way at service of prayer at a non-Catholic/non-Christian event and put in some place of honour or prominence, one is usually simply acknowledged in some form such as “[Title] So and So, [ecclesiastical office], honoured guest” or “[Title] So and So, [ecclesiastical office], envoy of _____”…the latter especially if one is asked to convey greetings or otherwise speak or act.