Marriage is an important part of society, however that ceremony is played out. Of course, individual attitudes towards getting married vary, requiring or engendering a wide variety of phrases, separate but not quite equal to each other.
In neutral terms, people get married or marry, possible derived from ancient word meaning young girl, referring only to the legal status itself. The modern understanding of this term does not specify taking a husband or wife. In more archaic terms, they betroth, coming from an old English root meaning truth, or even espouse, based on an old French root meaning to take as wife, but who would actually say those?
For those more pessimistic or even negative about the whole matter, a couple could tie the knot. This apparently derives from a Celtic tradition of a couple holding hands and making a figure eight together, following by a cord being attached between them, which was only cut when then ceremony was over. Getting hitched is a bit of quick decision based on the attaching (or hitching) of the wagon with the wife’s possessions to the fresh groom’s horse. The both apply a bit of fatalism about the whole matter. Still, that is better than a shotgun marriage, where the pregnant bride’s father insists on the groom doing the “right thing”, whether he wants to or not.
Since marriage is often more of a societal act than an individual choice, it has often reflected official status. So, the priest would join the couple in matrimony, meaning without his approval it does not count. Similarly, the father would bestow his daughter in marriage since women’s rights are a modern phenomenon in most places.
In more equal terms, modern independent couples walk down the aisle, at least in Christian circles. Even more egalitarian, they join together in marriage as is their right to do so.
Even if, as that old joke says, that the biggest cause of divorce is marriage, people keep on believing in synergy, i.e. 1 + 1 > 2.