I'm currently prepping a lecture on The Martyrdom of Polycarp for a JPBCL summer Greek reading group at Southern Seminary (See here, class description, syllabus). Here is a quote from Candida Moss that I find quite helpful from The Other Christs: Imitating Jesus in Ancient Christian Ideologies of Martyrdom.. Here she highlights the influence of the passion narratives on the composition of other martyrdom accounts in ancient Christianity.
“In order for the martyr to appear to be imitating Christ, he or she must be portrayed in as Christly a fashion as possible. The presentation of the martyr must cohere with the generally held presentation of Jesus in the passion narratives insofar as is possible. For the presentation to be effective, the author cannot drift too far from his or her audience’s understanding of scripture even as he or she seeks to reimagine and control it.”
From this, a few things come to mind. First, the author(s) of martyrdom accounts have an awareness of the passio narratives. Second, some martyrdom accounts possibly take historiographical liberties so as to reconfigure a martyr around the passio narratives. And third, if I may conjecture, martyrdom accounts communicate something of the spiritual status of the martyr.
 Candida R. Moss, The Other Christs: Imitating Jesus in Ancient Christian Ideologies of Martyrdom (Oxford, UK: Oxford University Press, 2010), 53.