In ancient Proto Indo European society, a young newly-married woman went to live with her husband's family. She was often put to work doing menial chores (perhaps unsurprising in a patrilineal culture) such as cooking and cleaning; and in fact she was called a bru, "cook" (and yes, that word is related to brew and broth.) The young bru married a dghem, a man. (The word dghem comes from the word for "earth", and is the ancestor of Latin homo "man".)
Later, among the Germanic tribes, she was called the bruthiz, and he was a gumaz. Still later, in Old English, she became the bryd (pronounced roughly "brood"), and he was a guma &mdash or more specifically a brydguma, to distinguish him from all those other gumas out there.
With the influence of the Norse and French invasions, vowels and words across English were vastly changed, and by Shakespeare's time bryd had become bride. Meanwhile another word, grome, "young man", had come into common use (no one is sure how or from where), and it became confused with Old English guma and crowded it out. When the dust settled guma was gone, and grome &mdash now changed to groom &mdash had taken its place next to bride (and, incidentally, in the stables, another place young men were often found in those days).
Spiritually bride is a word of fertility and springtime, bursting forth with energy and motion; but like wed, bride ends with D, the sound of doorways, edges, new beginnings. Groom, while just as full of energy and motion, is more concerned with grounded, earthy work, and the manifestation of growth.