Traditions differ less about how a wedding looks than about what event, exactly, brings the marriage into existence. The answers are not variations on a theme; they are different theories, and they produce different consequences when something goes wrong.
Catholic teaching locates the marriage in the consent of the two people. The couple are the ministers of the sacrament and the priest is a qualified witness. It follows that a defect in consent at the moment of the vows means there was never a marriage, and this is the whole basis of the declaration of nullity, which finds that nothing existed rather than ending something that did.
Islamic law locates it in a contract. Nikah requires an offer, an acceptance, witnesses, and a dower that is owed to the bride herself rather than to her family. A ceremony is customary and not necessary; no clergy are required; the document specifies obligations and may specify conditions the wife stipulates in advance, including conditions about divorce.
Jewish marriage joins two once-separate stages. Betrothal and marriage are now performed together under the canopy, effected by the giving of a ring before witnesses and accompanied by a written contract, read aloud, that sets out what the husband owes the wife and what she is owed if the marriage ends.
Hindu marriage is completed by an act rather than by words: the seventh of the steps taken together around the fire. Indian courts have had to decide cases on precisely this point, where a ceremony was begun and not finished.
Sikh Anand Karaj is four circuits of the Guru Granth Sahib while four hymns are sung, the scripture rather than an officiant standing as witness.
And the Quaker wedding removes the officiant entirely. The couple stand in the silence of a meeting for worship and declare themselves married, and everyone present signs the certificate. It is the clearest case in the West of a marriage created by a community's witness alone, and English law has recognised it since the eighteenth century.