No difference. In either case, a dead individual is put through a religious 'ceremony' they or their family members may not have wanted.
No. In one case, we have a ceremony performed in the name of known dead individual (dead and buried) whose name has been obtained despite explicit requests not to by one faith, conducted by the other faith in accordance to that other faith's institutional policies and procedures. In the other case, we have a prayer offered for an apparently mortally wounded, but possibly alive person, by an individual acting according to the immediate urgency of the moment.