Historically, wood and would arrive by different routes. Wood comes from Old English wudu, meaning timber, forest, or material from trees, a thoroughly physical word tied to building and fuel. Would comes from wolde, the past form of willan, meaning to want or wish. One grew out of the landscape; the other grew out of desire. Over centuries of sound change, their pronunciations collapsed into the same shape even though their meanings remained distinct. What survived was an accidental pairing: matter and intention sharing a soul.
At first glance, the two words seem to have little in common beyond pronunciation, but like seam and seem, they function as homophonyms*. Wood represents physical potential, raw material waiting to be shaped into something else. A table, a house, or a fire all exist in the wood before anyone acts on it. Would, by contrast, represents abstract potential. It describes actions that have not yet happened but could, given choice or circumstance. One belongs to the physical world and the other to the abstract one, yet both deal in what is possible rather than what already is.
That shared role explains why the pairing works. Things come from wood. Actions come from would. One requires tools; the other requires will. Just as a seam joins fabric and seem joins ideas, wood and would occupy parallel roles on different planes. English flattened their sounds and, in the process, quietly aligned matter and intention under a single pronunciation.
*I’m coining the term homophonym for a pair of words that sound alike, are spelled differently, and happen to converge in meaning or function, because English never bothered to give us a proper name for them.
Tom Bont's Silver Key 