[There is a] subtle distinction between Holy Matrimony and Marriage. The terms really ought not be used interchangeably, though they often are. However, marriage, properly speaking, is a human phenomenon (as part of the creation; and as many believe, thus instituted by God). Even given that source, there is wide variability to the form of marriage in many cultures and countries, through time and space, including the Jewish tradition out of which the Christian tradition grew. In many respects the Christian understanding of marriage was as much influenced by prevailing Roman custom (and law) as it was by Jewish understandings.
Holy Matrimony, or “Christian Marriage” is a particular subset of these various forms of marriage. The Canons of the Episcopal Church (I.18.1) attempt to preserve this distinction, limiting Holy Matrimony to marriages that are “entered into within the community of faith,” that is, within the church. (As a side note, I will point out that the BCP rubric, page 422, allowing “Christian marriage” in which only one of the parties is a Christian, pushes the envelope considerably, and is arguably discordant.)The Exhortation at the opening of the Celebration and Blessing of a Marriage, on the other hand, supports the distinction, noting that “marriage” has existed since the Creation, but that what the assembled body has “come together” for is Holy Matrimony. The Catechism, page 861, continues this clarification by stating, “Holy Matrimony is Christian marriage.” ...
Thus our church recognizes the existence of marriages which do not come under the law of our church as Holy Matrimony.
Read it all.
I note that Tobias points out the following rubric on page 422 of The Book of Common Prayer:
In the Episcopal Church it is required that one, at least, of the parties must be a baptized Christian ...
I've always found this rubric to be rather odd. How exactly does our Church expect an unbaptized person to live into a vocation whose vows deepen and contextualize the meaning of our baptismal covenant vows and which (as I understand Holy Matrimony) signifies a particular response to our Lord's invitation, "Follow me"? And on what grounds do we allow the unbaptized access to the sacrament of Holy Matrimony, but not to the sacrament of Holy Eucharist?