Vaughan Roberts (of St Ebbe's C of E the rector) preached a terrific sermon on Daniel 7 today - one that rang all sorts of bells in my thesis addled brian. He started with the martyr question: if I was in the situation of having to chose life or martyrdom, what would I do? The right answer is, of course, 'I don't know'... Why? Because martyrdom is not within our human power; and because it isn't about exercising courage.
And this was the earth-shattering point: it is about vision, aka faith. That is, the vision we get in Dan 7 - the vision of the temporary state of the empires and the sitting on the throne of the ancient of days, and the handing of authority to the Son of Man - is visible to the eyes of faith. And it is this vision - a revelation that is given, of course - of the way things truly are that makes it possible for the Christian to say 'I can be none other than what I am'. This is a vision of the providential work of God worked out in Jesus, the Son of Man.
So, what makes a martyr distinctively Christian is this vision of the rule and authority of God in Christ Jesus. Without that vision: nothing. Martyrdom (contra Aquinas) is the result of faith.