As Catholics, how should we use this word? To go by contemporary usage, a martyr could be anyone who died (or merely suffered) for any religion, or even any secular cause. Cf. dictionary.com:

1. a person who willingly suffers death rather than renounce his or her religion.

2. a person who is put to death or endures great suffering on behalf of any belief, principle, or cause: a martyr to the cause of social justice.

For the Church, however, martyr is an exalted title, reserved for the few who die in witness of the truth, which is Jesus Christ.

One can find cases that exist on the verge - those who died witness to some aspect of the natural law, the truths of reason, or to natural goods - such as the execution of Socrates. Such deaths, while honourable and dignified, cannot be considered the martyr's death; instead they may be called 'heroic' or 'noble'.

I urge you to resist the sloppiness and the implicit false universalism into which our degenerate language can lead us, and employ this title only as the Church herself employs it.