> One of those accounts uses a different name for him
I think you are probably remembering a (disputed) claim based on an edit made in a particular later copy that Tacitus (one of the earliest independent sources on both Christ and the early Christian community, particularly in Rome) referred to the Christian community in Rome as “Chrestians”, immediately before using the standard rendering of Jesus title as “Christus”. Even if Tacitus did use “Chrestians”, that name for the early community is attested in other sources (and even tied and used alongside Christian in some inscriptions from that community, IIRC), his reference to Christ did not use any alternate title,